Electricity And Magnetism:

Transcript

Electricity and Magnetism:  Magnetic effects of electric current  Magnetic field & field lines  Magnetic field due to a current carrying conductor  Force on a current carrying conductor in magnetic field  Magnetic Field due to Current carrying Circular Coil  Magnetic Field due to Solenoid  Electromagnetic induction  Electromagnet  Electric Bell  AC Generator or Dynamo  DC Generator  Electric motor DC /AC  Transformer Magnetic field & field lines: Magnetic lines of force:     Natural and Artificial Magnets Properties of a Magnet Magnetic Induction Neutral Points We have already seen little history of magnetism. Magnetic materials are found in nature. They are rich ores of iron, nickel and cobalt. We have learnt their properties. We have learnt the uses and applications of magnets. We have studied various materials and found out which materials can be used to prepare artificial magnets of desired strength. We also have mastered the fabrication of ceramic magnets of desired shape depending on the application. Still we refresh our understanding quickly. We work in a laboratory with bar magnets. They are normally 5 to 10 cm in length, 1 to 1.5 cm in width and 5 to 10 mm in thickness. Letters N and S are marked at two ends. Poles are identified by these letters. Sometimes only a dot is marked, generally it is the north pole. The best test to identify the poles is to suspend a magnet freely. North seeking pole is the north pole and south seeking pole is the south pole. Very first thing that we have learnt about magnet is that, magnets attract the pins, nails and other things which are made from the iron and steel. The central image below shows that many pins 1 can be attached to the magnet one below other. The second thing we learn is that like poles repell each other and unlike poles attract each other. The other two diagram below show the property of repulsion. Ring magnets are made to float on each other, it is a common toy. We see fingers of a child which makes bar manget float on other similar bar magnet. He has to prevent the upper magnet from turning. We see the two magnets connected to each other in central diagram. It is the example of unlike poles attract each other. Activity 1: Obtain two bar magnets, two lanthanium magnets, and four ring magnets from the local shop. Or from ‘Permag’, Wakdewadi, Pune-Mumbai Road (old), opposite Bajaj tower, Pune. Varify the things which are shown in above diagrams. Activity 2: Obtain a hard board, iron filings and two bar magnets. Verify the patterns shown in the diagram above and on the next page. Enjoy it. Co- relate them with schematic diagrams (diagrams with colored lines). We do some simple experiments with iron filings and magnets. We keep bar magnet below a hard board. Then we put a white paper on the hard board. We sprinkle some iron filings and gently tap the board. The iron filings arrange themselves in a specific way. We get the pattern shown above. We again take help of the concept ‘field’. Here we say space around a magnet possesses certain properties in presence of the magnet. Such space is said to possess ‘the magnetic field’. We try 2 to understand these patterns in terms of ‘lines of force’. The lines of force around a bar magnet are schematically shown in the second diagram. Following two pairs of the figures are showing us first the pattern of the iron filings on the white paper and then arrangement of the magnets. The diagram also shows the schematic pattern of the lines of the force. In first pair of diagram the like poles are facing each other and in second case the unlike poles are facing each other. The lines of force are imagined by seeing the patterns of iron filings. They also can be traced using small compass needles. This has led to conclude the nature of lines of force.**(19-10-13) Activity 3: Compass needles are available in market in size of half inch diameter and one inch diameter. Their cost is in range 2 to 5 rupees each. Obtain such compass needle. Keep the bar magnet on the plane white paper. Place a compass at a point near north pole. Mark two points near the south pole (point 1) and north pole (point 2) of the compass. Lift the compass needle. Keep it such that south pole matches with point 2. Now mark the point near north pole. This is point three. This way start from north pole and end at south pole. Draw at least 10 lines in each case and compare them with the above schematic diagrams. 3 When a bar magnet is cut in two pieces we get two small magnets. All properties of original magnet and two small magnets remain same. We do not get separate poles by cutting the magnet. Hence we say magnetic monopole does not exist. This shows that the magnetic lines of are continuous lines. In case of bar magnet the lines of force appear to ooze out from north pole and they appear to merge in south pole. Actually the lines are continuous in the material also. The electric lines of force start from the positive charge and merge in the negative charge. This is the main difference between magnetic lines of force and electric lines of force. Two most important properties of the magnetic field are as follows. I) Magnetic lines of force are continuous lines of force and II) Two lines of force never intersect with each other. This we will see in context of the field due to electric current also. Electricity and Magnetism: Introduction: Introduction: Magnetism and static electricity are known to mankind from many centuries. The real progress in the field of electricity and magnetism (rather electromagnetism) is happening from last 200 years. Hans Cristian Oersted first noticed in 1820 that a magnetic needle placed near a current carrying conductor shows a noticeable deflection. This deflection becomes prominent when the current is large and needle is near the conductor. He further noticed that the needle deflects in other way when the direction of the current is reversed. He carried extensive experiments. He concluded that ‘there exists magnetic field near the current carrying conductor.’ We now know that electric current is due to flow of electrons in the conductor. We have studied that the Electron is discovered in 1897 by J. J. Thompson. Electron was not known at the time of Oersted (1777-1851). The discovery of electron leads to conclude that ‘the moving charges induce (produce) magnetic field in its surrounding space.’ 4 We will try to learn the formulae relating current and magnetic field in few common situations. We must understand the difference in current and current element before we learn some formulae. We have defined the electric current as Electric Current: The rate of flow of charge is defined as the electric current flowing through the conductor. Where I is average current flowing through the conductor, Q is the total charge flown in total time‘t’. The SI unit of charge is ‘coulomb’ and time is ‘seconds’. The SI unit of current is Ampere. More precise definition of electric current or instantaneous current is given by the definition where ‘dq’ is the small amount of charge flown in small time ‘dt’. In both definitions ‘current is a scalar quantity’. Current Element: We note here that current exists in case of complete circuit. When we say that the current is passing through a straight conductor, such current carrying conductor is a part of the total circuit. The small part of the current carrying conductor can always be considered as a ‘straight’. Such current carrying small portion is called as the ‘current element’. It is denoted by ⃗⃗⃗⃗⃗ or ⃗⃗⃗⃗ . Here dx or dl is the length of the small element. In a given small element, we have to specify that current goes from one end to other end. Then only it is meaningful. Current always passes from higher potential to lower potential. Thus, the current element is the vector quantity. Biot and Savart studied this phenomenon in more detail. They found that the ‘magnetic field vector’ exists in a plane perpendicular to the current element. Biot-Savart’s law is stated as Biot-Savart’s law: The small amount of magnetic field ⃗⃗⃗⃗⃗ produced by the current element ⃗⃗⃗⃗ formula ⃗⃗⃗⃗ ⃗⃗⃗⃗⃗ 5 ̂ is given by the Where ⃗⃗⃗⃗⃗ is the magnetic field. Minimum distance from the current carrying conductor is denoted by ‘r’. ̂ is the unit vector in the direction of ‘r’. is the permeability of the space around the current element. The subscript ‘0’ denotes that the medium is air or ‘vacuum’. A current carrying conductor is shown in following diagram. It is vertical say along ‘z’ axis and the direction of current towards +ve ‘Z’. Point P is at distance ‘r’ in x-y plane. The small amount of magnetic field produced will be in x-y plane which is perpendicular to ⃗⃗⃗⃗ . The magnetic field ⃗⃗⃗⃗⃗ is pointing in the plane of paper. For a steady current I, the value of the magnetic field will be constant at constant distance r. Hence the magnetic field can be represented by concentric circles. It can be represented by two side diagrams. The Right hand rule: Imagine that you are holding a straight conductor in your right hand. Stretch the thumb along the length of the conductor and fold your fingers around the conductor. If stretched thumb shows the direction of current, then the folded fingers show the sense of magnetic lines of force. The direction of the magnetic field at a point is tangential to the circular line of force at that point. Magnetic lines of force: The concept of lines of force is used to understand the nature of ‘electric field’. Magnetic field is also expressed by the inverse square law- Biot Savart’s law. The inverse square nature of magnetic field is similar to electric field. Origin of electric field is ‘the charge’. We have seen that the origin of the magnetic field is in electric current. More accurately magnetic field is a result of moving charges. The concept of lines of force is also useful in understanding the nature of magnetic field. 6 We already have seen that the value of magnetic field at constant distance ‘r’ from a current carrying conductor is constant. The locus of the points having magnetic field of same magnitude is circle. The direction of magnetic field at a point is given by tangent to the circle at that point. Hence the nature of the magnetic field around a current carrying conductor is represented by the concentric circles around the straight conductor. It is shown in the above figure and also in the figures given below. The above diagrams show the lines of magnetic field around the conductor of circular loop. These diagrams are of same situation but in different orientation. The magnetic lines of force help us to understand the nature of the magnetic field. We can always find the magnitude and direction of the magnetic field by using various formulae. But while desing certain instrument, we need to know how the pattern of field is changing in specific volume of the space. This can be done by mapping lines of force in the given region of the space. For this it is essential to know the properties of lines of force. The properties of the magnetic lines of force can be summarised as follows:   Magnetic lines of force are circles. They start from a point and end into the same point. They are continuous lines. They do not intersect with each other. This is because magnetic field at a point has unique value and single direction. The intensity of Magnetic field is also defined in terms of magnetic lines of force. Intensity of Magnetic field (⃗⃗⃗ ): Intensity of magnetic field at a point is proportional to the number of perpendicular lines of force crossing unit area at that point. 1) Magnetic field due to straight conductor: Consider a straight conductor carrying current ‘i’ which is infinitely long. ⃗⃗⃗⃗⃗ is the current element of the conductor at Q. P is the point at distance ‘r’ from the conductor. PM is normal to the conductor. The current element ⃗⃗⃗⃗⃗ is at distance ‘x’ from M. The distance of point P from the current element is ‘l’. The angle between the current element and QP (l) is θ. The angle MPQ is ϕ. The situation is shown in the side diagram. 7 The intensity magnetic field at P due to the current element ⃗⃗⃗⃗⃗ ⃗⃗⃗⃗⃗ ⃗⃗⃗⃗⃗ ̂ ⃗⃗⃗⃗⃗ = ⃗⃗⃗⃗⃗ = since θ and ϕ are complimentary angles. The total magnetic field at P due to entire conductor is found by adding the effect of each current element. It means we first divide the conductor into elements of length ‘dx’. Find the effect of each current element at P, and then add these effects vectorially. All this process is named as ‘integration’ in mathematics. The symbol used for this process is∫ . This symbol is further made explicit depending on the process (partial integration, double integration etc.). Hence when we integrate ‘dx’ over the entire conductor we get total magnetic field ⃗⃗⃗⃗ at P. It is written as ⃗⃗⃗ = ∫ ⃗⃗⃗⃗⃗ =∫ = ∫ Note as angle ϕ changes from –π/2 to +π/2, it covers the length of conductor from - to + In this equation as we shift from one element to other element, the value of ‘x’ changes. Therefore, the value of ‘dx’ also changes. Similarly the value of ‘ϕ’ and the value of ‘l’ also change. It becomes difficult when we have more than one variable. We will substitute for ‘x’ i.e. ‘dx’ and ‘l’ in terms of constant ‘r’ and variable ‘ϕ’. This will simplify the process. = tan ϕ In triangle PQM x = r tan ϕ therefore dx = r sec2 ϕ dϕ and = cos ϕ l= l2 = 8 l2= r2 (sec Substituting the values of ‘dx’ and l2, we get ⃗⃗⃗ = ∫– dϕ ∫– = [sinϕ]-π/2π/2 = = ⃗⃗⃗ = [sin π/2 – sin (- π/2)] webers / m2 This equation clearly indicates that the field intensity falls as r increases. It is inversely proportional to distance. (⃗⃗⃗ ). Activity 4: We can verify this property (⃗⃗⃗ ) in laboratory. We require a power supply which can deliver 6V/5A or 12V/5A. We require high current source to see the magnetic effects. We need a straight copper conductor of diameter 3 to 5mm and minimum 20 cm in length, a variable resistor of same current capacity and a small compass needle of diameter 15 to 20 mm. Arrange the apparatus as shown in the side diagram. Make a hole to a hard board and pass a copper rod through it. Draw a horizontal line on the hard board from the conductor. You can stick a strip of graph paper on it. The copper rod can be kept vertical using rubber-corks and hard board is kept horizontal by using supports like books or weights in the laboratory. A rheostat having current capacity of 5A is connected in series for current control. A key is connected in the circuit or one may use on-off of power supply as a key. Make the arrangement as shown in the diagram. Place the compass as near as possible. Pass the current and note the reading. Move the compass away by 5mm, and note the deflection. This way we can make the observation table and verify the relation. Assignment 1: A current of 2 A is passing along z axis through a conductor. Imagine that this conductor is passing through the origin of X-Y plane. What is the magnitude and direction of the magnetic field at points I) (0.1,0) II) (0.1,0.1) and (0, 0.1). Find the value, state the direction of the vector and also plot it. [given: = 10-7 ] Use SI system of units. 9 Force on a current carrying conductor in magnetic field: A current carrying conductor is placed in a magnetic field. It is shown in the first diagram. It experiences force as shown. We will see the origin of this force. http://www.youtube.com/watch?v=HTTA30sEv6o Force on a charged particle moving in magnetic field: A charged particle having charge ‘q’ moving in magnetic field of intensity ‘ ⃗ ’ experiences a sideways force. The force is proportional to the strength of the magnetic field, the component of the velocity which is perpendicular to the magnetic field and the charge of the particle. This force is known as the Lorentz force, and is given by equation ⃗⃗⃗ = q x⃗ tesla. Since the force is given by cross product, force is perpendicular to the plane containing and ⃗ . This can be understood as follows. Any conductor contains lot of free charges. They move in a preferred direction when p. d. is applied to it. This is known as electric current. Each charge experiences the ‘Lorentz force’. The sum total of these forces is the net force on the current carrying conductor. Let ‘n’ be the number of charges per unit volume of the conductor. If ‘l’ is the length of the conductor and ‘A’ is its cross sectional area then the total number of charges ‘N’ are given by N = nlA. Hence the total force on the conductor is 10 = n l A q v B sinθ ⃗⃗⃗ = I l B sinθ where I = nAqv is the electric current. ⃗⃗⃗ = ⃗⃗⃗ X ⃗ The direction of the force is given by Fleming’s left hand Rule. Assignment 2: An electron is ejected from electron gun having accelerating potential 10V. Electron moves along +x axis. It passes through the magnetic field of strength 2.4T along +y direction. The length of the poles creating the magnetic field is 4 cm. In which direction the electron will shift? Calculate the displacement of the electron. [Hint: You need to calculate velocity of electron, time of flight in magnetic field, etc.] Fleming’s left hand Rule: Stretch the thumb, middle finger and index finger of the left hand so that they are mutually perpendicular to each other. If middle finger shows the direction of electric current ⃗ in the conductor, if index finger shows the direction of magnetic field ⃗ then the magnetic force ⃗⃗⃗ on the conductor is given by the stretched thumb. It is shown in the side diagram. Assignment 3: Two copper bars of diameter 5 mm are along the ‘x’ axis. They are separated by 3 cm. A brass bar of diameter 3 mm and length 5 cm rests on it. The mass of the brass bar is 3g. The coefficient of friction between two bars is 0.1. The uniform magnetic field of 3 tesla is applied along +z axis throuout the length of the copper bars. If the current of 5A is sent through the brass bar then will the brass bar move? If the coefficient of kinetic friction between brass and copper bars is 0.08 then what is the acceleration created in the bar? 11 2) Magnetic field due to current carrying circular coil: Consider a current carrying circular coil. Let ‘i’ be the value of the current flowing through it and ‘a’ be the radius of the coil. The coil is of single turn. Point P is along the axis at distance ‘b’ from the center of the coil. We will find the formula for the value of magnetic field at P due to current in this coil. Consider an element of length dl at point R. ⃗⃗⃗⃗ becomes the current element at R. Join RP. The distance RP is denoted by ‘r’. We are looking at coil with respect to point ‘p’, therefore current appears anticlockwise. RP or ⃗ is perpendicular to the plane of the coil. Hence the angle between current element⃗⃗⃗⃗⃗ and unit vector along ⃗ is 900. S According to Biot Savart’s law the small field ⃗⃗⃗⃗⃗ due to ⃗⃗⃗⃗ at P is given by ⃗⃗⃗⃗ ⃗⃗⃗⃗⃗ ̂ ⃗⃗⃗⃗⃗ ⃗⃗⃗⃗⃗ = The angle between ⃗⃗⃗⃗⃗ and ̂ is 900. Since sin 900=1, the value o ⃗⃗⃗⃗⃗⃗⃗ is given by above formula. ⃗⃗⃗⃗⃗ is perpendicular to the plane containing current element⃗⃗⃗⃗⃗ and ̂. If angle RPO is ϕ, then ⃗⃗⃗⃗⃗ also makes angle ϕ with the normal at P. ⃗⃗⃗⃗⃗ has a component ⃗⃗⃗⃗⃗ cosϕ along the normal at P (in upward direction) and ⃗⃗⃗⃗⃗ sinϕ along the axis. Consider a diametrically opposite current element at point S on the coil. The small field due to this element is shown by dotted line. It will have two components. The sine component will be along the axis. This will add to first component. The cosine component will be along the normal (in downward direction). This will be equal in magnitude and opposite in direction of upper component. Hence cosine components will cancel and only sine components will add along the axis. This is true for all current elements. Hence resultant field will be along the axis obtained by adding sine components. ⃗ =∫ = ∫ ⃗⃗⃗⃗⃗ 12 =∫ ⃗⃗⃗⃗⃗ = ∫ = (2πa) ⃗ = ⁄ weber /m2 This is the value of the field at point P due to a loop carrying current ‘i’. If the coil has ‘n’ turns then this value will be multiplied by ‘n’. There will be ‘n’ in the numerator. Assignment 4: A coil of radius 5 cm having 500 turns is mounted on a stand so that its plane is vertical. The plane of the coil is along the magnetic meridian. A current of two amperes is passed through the coil. A magnetometer having tiny magnet of length 2 cm is placed at 40 cm along the axis towards east from the center of the coil. Will the magnet of magnetometer orient itself along EW direction? If not, at what direction will it orient? Assume that magnetic field remains constant along vertical line to axis at a given distance. BH = 50 μT at the place of experiment. Magnetic field at the center of the coil: To find the field at the center of the coil i.e. at O, we put b=0. Then the formula for field ⁄ . becomes ⃗ = We note here that the direction of the field can be found easily again by using the right hand. Curl the fingers and stretch the thumb of the right hand. If tips of the curled fingers give the direction of the current in the loop, then the stretched thumb gives the direction of the magnetic field along the axis of the coil. Assignment 5: Consider the situation given in assignment 4. Now the magnetometer is placed at the center of the coil. Then what is zero-error for setting the magnetometer? Magnetic field at a point P along axis very far from the center: When point P is very far from O, b a. As a result, a2 becomes negligible compared to b2. Also b Hence the formula for magnetic field becomes ⃗ = 13 = = Where A = π = area of the loop. The quantity ‘i A’ in the numerator is defined as the ‘magnetic dipole moment of the loop’. Activity 5: We can easily verify relations qualitatively for the magnetic field in laboratory. Most of the laboratories possess ‘tangent galvanometer’. Remove the magnetometer from the center of the galvanometer. We require a power supply which can deliver 6V/3A or 12V/3A. If the coil of the galvanometer has marking of 5A terminal, then we need power supply of 5A capacity. It will give better results as high current source shows better magnetic effects. We need a meter scale, a variable resistor of adequate current capacity and a small compass needle of diameter 15 to 20 mm. Keep the meter-scale on the mount of magnetometer symmetrically. The mark of 50 cm of meter scale will coincide with the center of the coil. The meter scale will extend 50 cm on each side. It is along the axis of the coil. Keep the supports at the ends so that it should not bend at ends. Connect the power supply to coil through a rheostat of proper current capacity and plug key. Keep the compass needle at the center of the coil. Key is open. Note the position of the needle. It must be along NS direction. Adjust the plane of the coil along NS. Press the key and pass the current. Note the reading when compass needle is at the center. Now move the compass on the meter scale in steps. Note the reading in each position. It will be observed that the deflection of the compass needle will decrease as the coil goes away from the center. Hence the above equations get qualitatively verified. Magnetic Field due to Solenoid: Solenoid: It is a device in which metallic wire of desired cross section is closely wound around a cylinder. It produces uniform magnetic field when electric current is passed through the wire. Usually ferromagnetic core is used inside a cylinder to increase the strength of the magnetic field. Solenoids are important because they can create controlled magnetic fields and can be used as electromagnets. 14 Calculation of the field along the axis of a solenoid: Consider a solenoid as shown in the diagram. All practical solenoids are of finite length. Point P is on the axis inside the solenoid. We consider ‘a current element of length dx’ of the solenoid. Point P is at distance ‘x’ from the current element ‘dx’. We will see its effect at P. Then we will integrate it over the total length of the solenoid. Let N be the total number of turns in the solenoid and L be the length of the solenoid. Then i(N/L)dx will be the total current element. We have seen that the magnetic field at a point on the axis which is at distance ‘b’ from the center of the coil is given by ⃗ = ⁄ weber /m2 Where ‘a’ is the radius of the coil and ‘i’ is the current in the coil. The magnetic field ⃗ at point ‘P’ which is at distance ‘x’ from the element ‘dx’ becomes d⃗ = From figure, Substituting these values (-) a cosec2 ϕ dϕ. dx = (-) a cosec2 ϕ dϕ. = = (-) cosec2 ϕ dϕ. = - sinϕ dϕ Substituting this, equation becomes d⃗ sinϕ dϕ 15 dx = cot ϕ. Therefore x = a cot ϕ. Hence dx = - a cosec2 ϕ dϕ. ⁄ ⁄ We have to find the effect of total solenoid of length ‘L’ at P. For this, we need to add the effects of all elements of length ‘dx’ over the entire length of the solenoid. The variable on the right hand side in above equation is only angle ϕ. The entire length of the solenoid can be covered by ‘integrating’ right hand side over the limits  to . Hence we get ⃗ =-  ∫ ⃗ = cos] webers/m2 [cos - ------------ (X) Special case I: If the solenoid is long and point P is at the center of the solenoid, then   . Then [cos 0 – cos 180] = 2. Hence the value of the magnetic field becomes ⃗ = webers/m2 Special case II: If point P is at one end of the solenoid, then  [cos 90 – cos 180 ] = 1. Hence the value of the magnetic field becomes ⃗ = and  . Then webers/m2. Magnetic Flux: Consider that magnetic field is constant over some region. The intensity of the magnetic field is ⃗ . Imagine some area A’ is perpendicular to the lines of force of ⃗ The quantity magnetic flux is defined as Φ = ⃗⃗⃗⃗ (A) Area is also treated as a vector quantity. We will see it later. If ⃗⃗⃗ and are not perpendicular to each other then the dot product is taken’. Therefore flux will always be a scalar quantity and it is equal to the number of lines of force perpendicular to the unit area at that point. 3) Electromagnetic induction: In side diagram we see a wire carrying current. Arrow above the wire indicates that there exists current in the wire. There is magnetic needle below the wire. The wire is parallel to the length of 16 the needle. Oersted first observed that the magnetic needle deflects whenever there is current in the wire. When the current is switched off, the needle sets itself in the North-South direction. He did extensive experimentation and further found that ‘if the direction of current is reversed then the needle deflects in other sense or in opposite direction’. In all his experiments he found that the needle is neither attracted towards the wire nor it gets repelled. It deflects in its own plane. Activity 6: Ampere gave the explanation of this phenomenon. He stated that the magnetic field is produced in the space around current carrying conductor. It exists in a plane which is perpendicular to the current carrying conductor. This explains why the needle is not attracted towards the conductor. We have already seen the nature of magnetic field around a current carrying conductor. Oersted further found that changing magnetic field induces current in a coil. This can be verified with the help of simple equipment more effectively in laboratory. Activity 7: It requires a coil, a galvanometer, wires and a bar magnet. The side diagram shows that a galvanometer is connected to the coil. In the first diagram the magnet is shown steady. It is placed in the coil. The galvanometer shows zero deflection. Let us remove the one connection of the galvanometer. The magnet is taken out and again the galvanometer is connected. A bar magnet is oriented with North Pole in downward direction. As the magnet moves towards the coil, the pointer of the galvanometer deflects. Note the direction of the movement of the pointer. Also note the maximum deflection made by the pointer. This is shown in the diagram below. The arrow shows direction of movement of the magnet. Arrow is red in color; we need to see it carefully. We know that galvanometer deflects when some current is passed through it. Hence we conclude that ‘the movement of magnet towards the coil induces current in the coil. This current flows through the coil of the galvanometer also. Therefore galvanometer shows the deflection.’ Now take the magnet out of the coil slowly and move it more rapidly towards the coil. The pointer of the galvanometer will deflect on same side. The maximum deflection value increases. 17 It means the value of the current increases with rapidness though the magnet and the coil are same. Now we take out the magnet slowly again. We change its orientation. South pole is in downward direction. Let us move the South pole towards the coil. The pointer of the galvanometer deflects in opposite direction w. r. to previous situation. It means ‘if the direction of magnetic field is changed then direction of current induced in the coil also changes’. If we move the magnet rapidly, then the maximum deflection increases. This is true in this orientation also. Faraday’s Experiment: Electromagnetic induction was discovered independently by Michael Faraday and Joseph Henry in August 1831. The discovery is in the name of Faraday as he was first to publish the results. He wound two wires on opposite sides of an iron ring. One coil is connected to the battery and the other coil is connected to the galvanometer. The arrangement is as shown in the side diagram. When he connected the battery, the galvanometer showed sudden deflection. The galvanometer came to zero after the movement. Galvanometer showed zero as the steady current flown through the first coil. He observed the deflection in the opposite direction when the coil was disconnected. Galvanometer had again shown zero deflection when there was no current in the first coil. He repeated the experiment several times. He observed that the galvanometer shows deflection only when the circuit is made or when circuit breaks. It does not show any deflection when there is no current in the first coil or there is steady current in the first coil. He concluded that, this induction was due to the change in magnetic flux that occurred when the battery was connected and disconnected. Faraday explained electromagnetic induction using a concept of lines of force. Scientists initially rejected his ideas. Later Maxwell formulated mathematical base, then Faraday’s law was widely accepted. Activity 8: Generally, the LEDs glow with full intensity for 1.5 V. We require very simple equipment to demonstrate it. We require a strong magnet as shown in photograph on page ½ (diameter 10mm 18 and height 10mm), a plastic syringe 10ml or 15ml capacity, enameled copper wire (24/26 gauge and 5/6 m in length) and LED. Construction:      Remove the piston and confirm that magnet freely moves in the syringe. Cut 5mm part of the piston from top. This will function like a stopper to syringe. Put the magnet in the syringe and lock it by putting the stopper. Wind the wire on the syringe tightly. Apply cello tape so that the turns do not slip. Let two ends of length 5-6 cm hang. Remove the enamel of two ends and connect the diode. As far as possible solder the ends to ensure electrical contact. Apply the cello tape and fix the diode to the wall of the syringe. Move the magnet briskly and see what happens. Construct your explanation why the diode glows for certain frequency and why does it not glow below it. Faraday’s law: Whenever there is change in magnetic field associated with the coil, e.m.f. is induced in the coil. The amount of induced e. m. f. is directly proportional to rate of change of flux associated with the coil. When we use SI units, the constant of proportionality becomes one. Hence Here e. m. f. is in volts and ϕ is the magnetic flux associated with the coil. It is in Webers. Heinrich Lenz in 1834 studied the phenomenon in more details. He gave the direction of the induced EMF and induced current resulting from electromagnetic induction. Lenz’s law states that Lenz’s law: The e. m. f. (and current) induced in the circuit is such that it always opposes the ‘cause’. Hence the equation becomes ------Volts The convention for currents is ‘all currents which are anticlockwise are treated as positive and corresponding e.m.f is also positive.’ The clockwise current and e.m.f. causing clockwise current are treated as negative. It is the accepted convention. (It may be because anticlockwise currents 19 generate the magnetic field in the positive ‘z’ direction, and clockwise currents generate the field in negative ‘z’ direction.) The convention is w. r. to viewer. It is clear that the ‘flux’ which is pointed towards the viewer is taken as positive and flux that goes away from the viewer is treated as negative. Consider two coils one above the other. A battery and a key are connected to lower coil. A clockwise current flows in a lower coil when the key is pressed. Magnetic field increases in negative ‘z’ direction. This changing magnetic field induces current in upper coil. According to Lenz’s law, the direction of induced current is such that it opposes the cause. It means, increasing field in negative ‘z’ direction must be opposed. So field due to current in upper coil must be in positive ‘z’ direction. Hence the current in the upper coil must be anticlockwise. This is the true meaning of the negative sign. Lenz’s law on the basis of ‘Law of conservation of Energy’: Consider the above situation again. Let us assume that our new circuit does not obey Lenz’s law. The equation for this circuit is without negative sign. . As we press the key, the current in the lower coil builds in clockwise sense. In our present circuit, the induced current does not oppose but assists the cause. It means the direction of the induced current is such that the magnetic field due to induced current will also increase in negative ‘z’ direction. This increases flux associated with first coil. Hence current in first coil will increase. The current in first coil will further increase magnetic field and induced current. The process becomes cyclic. The currents may be so large that the coil will burn. It may generate more energy than the battery energy within a short time. This is against the law of conservation of energy. Since the circuit has to obey ‘law of conservation of energy’; the current in the upper loop must oppose the cause i.e. it must be anticlockwise. There must be negative sign in the equation. Hence the equation remains as ------Volts If there are ‘N’ turns of the coil then the equation becomes Assignment 6: A strong magnet has a field of 5 T just outside the pole. It is kept along the axis of a coil. It produces a field of 1T at the center of the coil. The coil has radius 5 cm and has 500 turns. An ammeter of range 500 mA and having a resistance of 50 Ω is connected to the coil. When the 20 magnet advances to the center of the coil in 1.5 s then will the pointer of ammeter go out of range? If not, what will be the maximum reading in ammeter? http://www.youtube.com/watch?v=AuqfF2Mu3b4 http://www.phys.ttu.edu/~xbrll/Ch_21.pdf http://www.launc.tased.edu.au/online/sciences/physics/Lenz's.html http://www.youtube.com/watch?v=bkSsgTQOXVI http://www.absorblearning.com/media/item.action?quick=7d It is clear from the above formula that the value of the induced e. m. f. increases when    Number of turns of the coil increase. The magnetic field associated with the coil increases. The relative motion between the coil and magnetic field becomes more rapid or faster. Applications of Faraday’s law: Faraday’s law is one of the most basic laws in Electromagnetism. It has large number of applications. Most important applications are as stated below.      Electrical Transformers: The devices increase or decrease the applied a. c. voltage. They are used at generation stations, distribution systems, in all power supplies etc. Electrical Generators: Electrical generators convert mechanical or heat energy in electrical energy. It is based on the principle of induction. Induction cookers: It uses the principle of induction and also of eddy currents. The current in the coil is changed. It induces secondary currents (eddy currents) in the container. It is one of the fastest ways of cooking. Meters: Many types of flow meters for measuring blood flow, liquid flow are based on the principle of induction. Musical instruments: Speakers, microphones, electric guitar, electric violin use the principle of induction. Electromagnet: Activity 9: You require simple material which is at hand. A battery, a nail of 2.5 cm to 4 cm in length, few paper clips or paper pins, insulated copper wire of 16 to 20 gauge having length 50 cm to 100cm and rubber band. Copper wires which are used in transformer or motor rewinding should be used. 21       Wind the copper wire closely on the soft iron nail. Make the two ends of the wire of length about 7 to 10 cm in length straight. Use a common shaving blade to clean up the ends. Ends look pale red. The color of enamel coated wire is dark (blackish) red. Pale red is the color of pure copper. Connect one end of copper wire to negative of the battery and fix it with the rubber band. Keep some paper clips or pins near the end of the nail. Connect the other end of the wire to the positive end of the battery. Observe what you see. Disconnect one end of the battery. What do you see? Do all clips or pins fall immediately? Or do they take some time to fall? What do a wrecking yard, a rock concert and your front door have in common? They each use electromagnets, devices that create a magnetic field through the application of electricity. Wrecking yards employ extremely powerful electromagnets to move heavy pieces of scrap metal or even entire cars from one place to another. Doors use small magnets to keep the door closed. Electromagnets are used to amplify the sound coming out of speakers. And when someone rings your doorbell, a tiny electromagnet pulls a metal clapper against a bell. Mechanically, electromagnets are pretty simple. It consists of conductive wire, usually copper, wound around a piece of ferromagnetic metal as per required design. Current is passed, either 22 from a battery or from another source of electricity. This creates a magnetic field around the coiled wire, magnetizing the core as if it were a permanent magnet. Electromagnets are useful because you can turn the magnet on and off by completing or interrupting the circuit, respectively. The important character of the core is its magnetic field should reduce to zero in minimum time after disconnecting the current. The core should not get heated due to current in it. You can see various applications of ‘electromagnets’ in the link given below. http://atschool.eduweb.co.uk/heathsid/emk.html Electric Bell: Above picture is doorbell with opened cover and its schematic diagram. There exists the cover to protect user from the electric shock and instrument from dust and insects. The cover is opened so that you can compare the schematic diagram on left hand side and actual instrument in use. In schematic diagram U is the battery. Here battery shown is dc battery. But door bells can be designed to work on ac mains. K is the key, it is normally a push button. It is ‘push to on’ type. It has a inbuilt spring. It takes the button to normally off position as soon as the finger pressure is released. Push button connects the battery and copper wire in the electromagnet. E is the electromagnet. It has a copper wire wound around the two arms of the magnetic core. The wire is connected to one end of the flexible arm ‘A’. Flexible arm has a soft iron piece exactly in front of electromagnet. The other end of the arm has a small metallic ball. It hammers the gong B. T is the crucial part of the circuit. It is also called as the ‘make and break’ arrangement. It has adjustable screw. The tip of the screw touches the strip in front. Sometimes the tip of the screw and strip further get connected by silicon contacts. The silicon contact has high melting point and high working life. The working of the doorbell is simple. When the button K is pushed in, the circuit gets connected. The current in the copper wire passes and the electromagnet gets magnetized. It attracts the soft iron piece on flexible arm A. The small ball hammers on the gong B creating sound. As the arm A is attracted towards the electromagnet E, the contact at T breaks. This breaks the circuit. The current in the coil goes to zero. The electromagnet loses its magnetization. 23 The arm A becomes straight and comes to original position due to its elastic properties. The contact at T is now made. The circuit is made. The process becomes cyclic and the gong gets hammered after definite intervals. As a result, we listen the bell this key K is pushed. These days’ buzzer bells are not used. The sound is not pleasant rather it is irritating. Ding dong bells are used these days. http://www.youtube.com/watch?v=qMB5nQmB82M A common ding dong unit consists of two flat metal bars. They are bent at right angles at the ends as seen in the side picture. These bars are struck by plungers operated solenoid. The flat bars are tuned to two pleasing notes. When the doorbell button is pressed, the first solenoid's plunger strikes one bar. We listen sound of one tone. When the button is released, a spring on the plunger pushes the plunger up. It strikes to other bar, creating other tone. Thus a two-tone sound ("ding-dong") is created. It sends the proper signal to people inside and less irritates comparatively. AC Generator or Dynamo: Principle: A.c. generator is based on the principle of electromagnetic induction. Whenever there is change in magnetic field associated with the coil, e.m.f. is induced in the coil. The e.m.f. exists till the change in flux continues. The direction of the induced e.m.f. is given by the Fleming’s left hand rule. Construction: We refer to both diagrams shown below. First diagram is 3dimentional perspective and second diagram is schematic. The main parts are listed as follows. Armature: ABCD is the rectangular armature coil wound around the laminated soft iron core. The core is cylindrical as shown in the first diagram. The axis of the coil is shown by the dotted line at the center. Armature coil can be rotated by external mechanical agency about this axis. In case of hydroelectric power plant, the armature coil is rotated by rotating water turbine. In case of thermal power plant, the coil is rotated by the steam turbine. 24 Field Magnets: N and S are the poles of the magnet in which the coil rotates. The plane of the coil is perpendicular to the magnetic field. For this, we require cylindrical pole pieces. It is not shown in the side diagram. In case of big power stations the magnets are electromagnets. Slip rings: R1 and R2 are two metal rings. They are connected to the two ends of the coil. These rings rotate with the armature coil. Brushes: B1 and B2 are two brushes. In 3D diagram the brushes are shown by ‘a’ and ‘b’. They exert light pressure due to elastic (or spring) property. It ensures the electrical contact between the brushes and the rings. Brushes are connected to components in external circuit. Theory and working: Armature coil is rotated in magnetic field. The flux associated with the coil changes continuously. E. m. f. is induced in the coil. This is connected to external circuit and current flows in external circuit. The direction of the current is given by the Fleming’s left hand rule. The output of the generator between B1 and B2 is alternating. We can understand this if we concentrate on one arm say AB (or CD) of the coil. The coil is rotating with constant angular speed ω. Let us understand that field increases as the conductor approaches pole N. Hence field increases for quarter cycle, during which induced e. m. f. increases. In next quarter cycle, the field decreases, and therefore emf decreases. The polarity remains same. As the arm AB approaches pole S, the field increases in opposite direction. Hence the emf increases with opposite polarity. In next quarter cycle the emf decreases. As the coil rotates for one complete rotation, emf also completes one cycle as zero to maxima, maxima to zero in first half rotation. Then changes the polarity, goes to negative maxima of same value and comes back to zero. The output emf is sin wave. It is shown by the graph at the end of the formula. Magnetic flux associated with the coil is given by = .⃗ = N A B cos θ where N is the number of turns of the coil. e=e=25 ω = ϕ/t e=e = NBA [- ] e = NBAω sinωt e = e0 sinωt where e0 = NBAω It is clear from the formula that induced emf can be increased by increasing any one of the term or combination of (N) the number of turns of the coil, (B) the magnetic field, (A) the area of cross section of the coil and /or (ω) the angular velocity. The current flowing in the external circuit with load resistor R, is given by I= I= I = I0sinωt where I0 = Diagram relating the position of coil in a magnet and emf generated. http://www.ncert.nic.in/html/learning_basket/electricity/electricity/machine/dc_generator.htm http://www.youtube.com/watch?v=pIbSMpHQ9a8 http://www.youtube.com/watch?v=DCYB5DWeCng Assignment 7: In a small hydropower station the peak value of power generated is 1MW. The water turbine moves with frequency 400 rpm. The area of the coil is 1m2. The poles are more than 1M apart and the average strength of the magnetic field is 0.5T. The number of turns of the coil is 50. The safe current density of the copper is 1900 A per square inch. Then calculate the diameter (in cm) of the copper cable required for winding. 26 Direct Current Generator: www.electrical4u.com/principle-of-dc-generator/ ‎http://www.youtube.com/watch?v=gYiI6i9Zq4Y Note: Principle of the DC generator is same as AC generator. In construction also it is very much similar. There is change in type of rings only. The result is that, we get varying direct current in the load resistor. The nature of the output is shown in the second diagram. Mathematical formula is also similar to have positive values only. Hence we will only discuss the parts which change and thus the change in result that we get. A student is expected to make a detailed note for dc generator just like the ac generator by changing the description of rings and then the graph. You may leave the derivation. Slip Rings: The diagram of the slip rings is as shown in the diagram below. In spite of two rings, one cylindrical ring is cut in to two pieces. Each piece is connected to one end of the coil of the armature. There is separation between two halves. These half cylinders rotate with the armature. There are two metal brushes making electric contact. The electric contact is ensured by the metal sprigs which are located in brush holders. The total arrangement is also called as the commutator because it converts a. c. in to d. c. Let us understand this w. r. to above colored diagram. The arm of the armature coil near the north pole is always in contact with brush on right side and the arm of the armature which is near the south pole is always in contact with the left brush. If we assume that the current is 27 coming out from the arm near the north pole then current will always rush from right to left in the external resistor. The value of the current is varying because the flux cut by the coil varies. But the direction always remains the same. Hence the generator is called as the DC generator. Electric motor DC /AC: http://www.animations.physics.unsw.edu.au/jw/electricmotors.html http://www.wisc-online.com/objects/ViewObject.aspx?ID=IAU11508 An electric motor is an electric machine that converts electrical energy into mechanical energy. Electric motors has large applications as industrial fans, blowers and pumps, machine tools, household appliances, power tools, and disk drives, etc. Small motors may be found in electric watches. They can work on DC battery supply or even ac supply. The largest of electric motors are used for ship propulsion, pipeline compression and pumped-storage applications with ratings reaching 100 megawatts. Cutaway view through stator of induction motor. The theoretical principle behind production of mechanical force by the interactions of an electric current and a magnetic field was discovered by André-Marie Ampère in 1820. The conversion of electrical energy into mechanical energy by electromagnetic means was demonstrated by the British scientist Michael Faraday in 1821. 28 The principle of the DC motor can be understood with the help of the side diagram. The electric current is supplied by the battery through brushes which touch the two half cylinders. In diagram the semi-cylinder towards us is negative and away from us is positive. Hence the current in the coil is clockwise. The magnetic field is from N pole to S pole. It is shown by the blue arrow. Appling the Fleming’s left hand rule the force on the conductor towards us (near north pole) is downwards while force on the conductor near south pole is in upward direction. The forces are shown by green arrows. This creates the torque on the coil. This torque rotates the armature in clockwise sence. The split rings maintain the polarity. Hence the current is always clockwise in the coil when seen from the top. This always rotates the coil and hence the armature in clockwise when seen from the brush side. Construction: Jedlik discovered the devices stator, rotor and commutator. These are the three main components of practical DC motors. Stator: The stationary part is the stator. Usually stator has either windings or permanent magnets. We can see the windings in the cylindrical cavity of the stator. The current passes through these windings when motor is connected to electric supply. It produces the magnetic field. The motors for which stator has winding possesses permanent magnets on the rotor. Two magnetic fields interact with each other and create torque on the rotor. The result is rotor rotates as per design. Rotor Rotor is the moving part in an electric motor. It turns the shaft to deliver the mechanical power. The rotor usually possesses permanent magnets if the stator has electric windings. Or the windings are mounted on the rotor central part for the motors whose stators possess permanent magnets. The two magnetic fields interact with each other and generate the forces that turn the shaft. 29 In mechanical construction of the motor the shaft of the rotor is always mounted on two bearings. This reduces the friction and increases the mechanical efficiency of the motor. The motors possess the winding of copper wire insulated with good quality enamel. It has high resistivity as well as it withstands for high temperatures. The layer of the insulation is very thin. It reduces the size of the motor as well as it maintains uniformity of the magnetic field. There is always a small air gap between the rotor and stator. The performance of the motor is better when the air gap is smaller. Application of electric motors revolutionized industry. Every machine is equipped with its own electric motor. It provides easy control at the point of use, and improves power transmission efficiency. Electric motors applied in agriculture eliminated human and animal muscle power for handling grain or pumping water. Household uses of electric motors reduced heavy labor, improved convenience and comfort. Today, electric motors stand for more than half of the electric energy consumption. AC motors: Practical rotating AC induction motors were independently invented by Galileo Ferraris and Nikola Tesla. Tesla demonstrated working motor in 1887. In 1888, Tesla presented his paper on electric motor and he is considered as the inventor of a.c. motor. Mikhail DolivoDobrovolsky invented the three-phase cage-rotor induction motor in 1889. This type of motor is now used for the vast majority of commercial applications. Tesla's motor was not practical because of two-phase pulsations. Induction motor improvements flowing from these inventions and innovations were such that a 100 horsepower (HP) induction motor currently has the same mounting dimensions as a 7.5 HP motor in 1897. Notes: The electric ac motors today have following properties as per the application. 1. Rotation is independent of the frequency of the AC voltage. 2. Rotation is equal to synchronous speed (motor stator field speed). 3. Variable-speed operation. Motors work on single-phase supply or with three-phase supply. Both types are available. Single phase motors with limited power are used in domestic application like mixers, grinders etc. Three phase and single phase motors are widely used in industry. 30 activity DC motor.doc ac motor.docx Transformer: Principal: A transformer is a static electrical device that transfers energy by inductive coupling between its winding circuits. A varying current in the primary winding creates a varying magnetic flux in the transformer's core. This flux is linked with secondary windings or coil through ferromagnetic core. This varying magnetic flux induces a varying electromotive force (emf) or voltage in the secondary winding. The induced voltage depends on the number of turns of the secondary coil. Thus transformers are basically of two types (i) Step-down transformers and (ii) step – up transformers. When the voltage across secondary is less than voltage across primary, then the transformer is called as the step-down transformer. When the voltage across secondary is more than voltage across primary, then the transformer is called as the step-up transformer. There is one more class of transformers called as ‘isolation transformers’. They are used to isolate the input and output circuits. The ideal transformer: The transformer in which there is no loss of energy at all is defined as the ideal transformers. In case of ideal transformer the energy in primary circuit is equal to the energy of secondary circuit. This is possible only when the flux associated with primary coil is totally linked with the secondary coil. The circuit diagram of ideal transformer is as shown in the side diagram. Consider the ideal, lossless, perfectly-coupled transformer shown in the circuit diagram. Let NP and NS be the number of turns of primary and secondary respectively. The ideal transformer induces secondary voltage ES =VS in proportion with the primary voltage VP = EP and number of turns. The respective equation is given by = = =a where, - VP/VS = EP/ES = a is the voltage ratio and NP/NS = a is the winding turns ratio. The transformer is step down if a ; and the transformer is step up if a Negative sign indicates that the primary and secondary voltages are out of phase by 1800. 31 The load resistor RL or load impedance ZL is connected across the secondary. The current flows in the load resistor. Let Ip and Is be the currents in the primary and secondary respectively. The power in the primary coil and secondary coil are same at any instant for ideal transformer. Therefore we can write Ip X Vp = Is X Vs Combining the two equations we get ideal transformer identity = = =a It is clear from the formula that the voltage ratio and winding turn ratio both are inversely proportional to the corresponding turn ratio. Induction law: The transformer is based on two principles: first, that an electric current can produces magnetic field and second that a changing magnetic field within a coil of wire induces a voltage across the ends of the coil (electromagnetic induction). Changing the current in the primary coil changes the magnetic flux that is developed. This changing magnetic flux in primary coil is linked with the secondary coil by the ferromagnetic core. The changing magnetic flux induces a voltage in the secondary coil. We refer to the diagram on left side. The primary coil is shown in red color while secondary coil is shown in blue color. These wires are insulated by enamel. It is high quality insulator. It creates high quality insulating cover on copper wire with minimum thickness. This reduces size of the transformer. Wires are tightly wound around the ferromagnetic core. The core is laminated. The function of the core is to link the flux generated in the primary totally to secondary. The voltage induced across the secondary coil may be calculated from Faraday's law of induction, which states that: Vs = Es = Ns where Vs = Es is the instantaneous voltage, Ns is the number of turns in the secondary coil. The term dΦ/dt denotes the change in magnetic flux Φ through one turn of the coil. We have already seen that the flux ϕ = ⃗ . ⃗ . Since the same magnetic flux passes through both the primary and secondary coils in an ideal transformer the instantaneous voltage across the primary winding equals Vp = Ep = Np 32 Taking the ratio of the above two equations gives the same voltage ratio and turns ratio relationship shown above, that is, = = =a http://ludens.cl/Electron/trafos/trafos.html Assignment 8: In a certain step down transformer the property of the core is that it requires 10 turns per volt. The frequency of ac mains is 50 Hz and voltage is 240V. If we have to build 12V- 6W ac mains transformer, then calculate the number of turns of the primary winding and secondary winding. Also calculate minimum value of the resistance that needs to be connected in secondary circuit for the proper function of the transformer. The nature of core laminations: There are many types of laminations namely E-I, L, U-I etc. Laminations are arranged in such a way that the magnetic circuit is complete in the plane of lamination. The paint applied to these laminations provides large electric resistance in a plane perpendicular to plane of laminations. This reduces eddy currents, prevents transformer from heating and increases the efficiency. We will see this in more details in higher classes. Here is the picture of E- I laminations. Note the width of the middle arm is exactly double than that of upper or lower arm of the E. This maintains the flux density in the core. E-I laminations are available in standard sizes. The power of the transformer decides the area of the central part of lamination stack. The size of the bobbin depends on it. Hence power of the transformer decides the size of the lamination and the size of bobbin. This is the part of the transformer design. We will see it in higher standards. The manufactures always supply the laminations as per your design if the requirement is in bulk. Molded Bobbins: This is the photograph of the standard size bobbins. They are made from the tough plastic. The material stands for rise in temperature of the transformer when it is in use. The manufactures always supply the bobbins as per your design if the requirement is in bulk. 33