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15.7 The Fig.Q.15.7 shows a coil of wire in the xy plane with a magnetic field directed along the y -axis.Around which of the three coordinate axes should the coil be rotated in order to generate an emf and a current in the coil?
15.7 The Fig.Q.15.7 shows a coil of wire in the xy plane with a magnetic field directed along the  y -axis.Around which of the three coordinate axes should the coil be rotated in order to generate an emf and a current in the coil?

15.7 The Fig.Q.15.7 shows a coil of wire in the xy plane with a magnetic field directed along the y -axis.Around which of the three coordinate axes should the coil be rotated in order to generate an emf and a current in the coil?

15.17 a) Can a step-up transformer increase the power level?
 15.17 a) Can a step-up transformer increase the power level?

15.17 a) Can a step-up transformer increase the power level?

15.16 A copper ring has a radius of 4.0 \mathrm{~cm} and resistance of 1.0 \mathrm{mS} . A magnetic field is applied over the ring perpendicular to its plane. If the magnetic field increases from 0.2 \mathrm{~T} to 0.4 \mathrm{~T} in a time interval of 5 \times 10^{-3} \mathrm{~s} what is the current in the ring during this interval?(Ans: 201A)
 15.16  A copper ring has a radius of  4.0 \mathrm{~cm}  and resistance of  1.0 \mathrm{mS} . A magnetic field is applied over the ring perpendicular to its plane. If the magnetic field increases from  0.2 \mathrm{~T}  to  0.4 \mathrm{~T}  in a time interval of  5 \times 10^{-3} \mathrm{~s}  what is the current in the ring during this interval?(Ans: 201A)

15.16 A copper ring has a radius of 4.0 \mathrm{~cm} and resistance of 1.0 \mathrm{mS} . A magnetic field is applied over the ring perpendicular to its plane. If the magnetic field increases from 0.2 \mathrm{~T} to 0.4 \mathrm{~T} in a time interval of 5 \times 10^{-3} \mathrm{~s} what is the current in the ring during this interval?(Ans: 201A)

15.8 How would you position a flat loop of wire in a changing magnetic field so that there is no emf induced in the loop?
 15.8  How would you position a flat loop of wire in a changing magnetic field so that there is no emf induced in the loop?

15.8 How would you position a flat loop of wire in a changing magnetic field so that there is no emf induced in the loop?

15.14 The back emf in a motor is 120 \mathrm{~V} when the motor is turning at 1680 \mathrm{rev} per min. What is the back emf when the motor turns 3360 rev per min?(Ans: 240 V)
 15.14  The back emf in a motor is  120 \mathrm{~V}  when the motor is turning at  1680 \mathrm{rev}  per min. What is the back emf when the motor turns 3360 rev per min?(Ans: 240 V)

15.14 The back emf in a motor is 120 \mathrm{~V} when the motor is turning at 1680 \mathrm{rev} per min. What is the back emf when the motor turns 3360 rev per min?(Ans: 240 V)

Example 15.5: A solenoid coil 10.0 \mathrm{~cm} long has 40 turns per \mathrm{cm} . When the switch is closed the current rises from zero to its maximum value of 5.0 \mathrm{~A} in 0.01 \mathrm{~s} . Find the energy stored in the magnetic field if the area of cross-section of the solenoid be 28 \mathrm{~cm}^{2} .
Example 15.5: A solenoid coil  10.0 \mathrm{~cm}  long has 40 turns per  \mathrm{cm} . When the switch is closed the current rises from zero to its maximum value of  5.0 \mathrm{~A}  in  0.01 \mathrm{~s} . Find the energy stored in the magnetic field if the area of cross-section of the solenoid be  28 \mathrm{~cm}^{2} .

Example 15.5: A solenoid coil 10.0 \mathrm{~cm} long has 40 turns per \mathrm{cm} . When the switch is closed the current rises from zero to its maximum value of 5.0 \mathrm{~A} in 0.01 \mathrm{~s} . Find the energy stored in the magnetic field if the area of cross-section of the solenoid be 28 \mathrm{~cm}^{2} .

15.14 Can an electric motor be used to drive an electric generator with the output from the generator being used to operate the motor?
15.14 Can an electric motor be used to drive an electric generator with the output from the generator being used to operate the motor?

15.14 Can an electric motor be used to drive an electric generator with the output from the generator being used to operate the motor?

15.17 A coil of 10 turns and 35 \mathrm{~cm}^{2} area is in a perpendicular magnetic field of 0.5 \mathrm{~T} . The coil is pulled out of the field in 1.0 \mathrm{~s} . Find the induced emf in the coil as it is pulled out of the field.
15.17 A coil of 10 turns and  35 \mathrm{~cm}^{2}  area is in a perpendicular magnetic field of  0.5 \mathrm{~T} . The coil is pulled out of the field in  1.0 \mathrm{~s} . Find the induced emf in the coil as it is pulled out of the field.

15.17 A coil of 10 turns and 35 \mathrm{~cm}^{2} area is in a perpendicular magnetic field of 0.5 \mathrm{~T} . The coil is pulled out of the field in 1.0 \mathrm{~s} . Find the induced emf in the coil as it is pulled out of the field.

15.13 It is desired to make an a.c generator that can produce an emf of maximum value 5 \mathrm{kV} with 50 \mathrm{~Hz} frequency. A coil of area 1 \mathrm{~m}^{2} having 200 turns is used as armature. What should be the magnitude of the magnetic field in which the coil rotates?(Ans: 0.08 \mathrm{~T} )
 15.13  It is desired to make an a.c generator that can produce an emf of maximum value  5 \mathrm{kV}  with  50 \mathrm{~Hz}  frequency. A coil of area  1 \mathrm{~m}^{2}  having 200 turns is used as armature. What should be the magnitude of the magnetic field in which the coil rotates?(Ans:  0.08 \mathrm{~T}  )

15.13 It is desired to make an a.c generator that can produce an emf of maximum value 5 \mathrm{kV} with 50 \mathrm{~Hz} frequency. A coil of area 1 \mathrm{~m}^{2} having 200 turns is used as armature. What should be the magnitude of the magnetic field in which the coil rotates?(Ans: 0.08 \mathrm{~T} )

15.5 Does the induced emf always act to decrease the magnetic flux through a circuit?
 15.5 Does the induced emf always act to decrease the magnetic flux through a circuit?

15.5 Does the induced emf always act to decrease the magnetic flux through a circuit?

15.6 When the switch in the circuit is closed a current is established in the coil and the metal ring jumps upward (Fig.Q.15.6). Why?Describe what would happen to the ring if the battery polarity were reversed?Fig. Q. 15.6
 15.6  When the switch in the circuit is closed a current is established in the coil and the metal ring jumps upward (Fig.Q.15.6). Why?Describe what would happen to the ring if the battery polarity were reversed?Fig. Q.  15.6

15.6 When the switch in the circuit is closed a current is established in the coil and the metal ring jumps upward (Fig.Q.15.6). Why?Describe what would happen to the ring if the battery polarity were reversed?Fig. Q. 15.6

15.16 Four unmarked wires emerge from a transformer. What steps would you take to determine the turns ratio?
15.16 Four unmarked wires emerge from a transformer. What steps would you take to determine the turns ratio?

15.16 Four unmarked wires emerge from a transformer. What steps would you take to determine the turns ratio?

15.17 b) In a transformer there is no transfer of charge from the primary to the secondary. How is then the power transferred?
 15.17 b) In a transformer there is no transfer of charge from the primary to the secondary. How is then the power transferred?

15.17 b) In a transformer there is no transfer of charge from the primary to the secondary. How is then the power transferred?

15.12 A generator has a rectangular coil consisting of 360 turns. The coil rotates at 420 rev per min in 0.14 \mathrm{~T} magnetic field. The peak value of emf produced by the generator is 50 \mathrm{~V} . if the coil is 5.0 \mathrm{~cm} wide find the length of the side of the coil.(Ans: 45 \mathrm{~cm} )
15.12 A generator has a rectangular coil consisting of 360 turns. The coil rotates at 420 rev per min in  0.14 \mathrm{~T}  magnetic field. The peak value of emf produced by the generator is  50 \mathrm{~V} . if the coil is  5.0 \mathrm{~cm}  wide find the length of the side of the coil.(Ans:  45 \mathrm{~cm}  )

15.12 A generator has a rectangular coil consisting of 360 turns. The coil rotates at 420 rev per min in 0.14 \mathrm{~T} magnetic field. The peak value of emf produced by the generator is 50 \mathrm{~V} . if the coil is 5.0 \mathrm{~cm} wide find the length of the side of the coil.(Ans: 45 \mathrm{~cm} )

15.3 A coil of wire has 10 loops. Each loop has an area of 1.5 \times 10^{-3} \mathrm{~m}^{2} . A magnetic field is perpendicular to the surface of each loop at all times. If the magnetic field is changed from 0.05 \mathrm{~T} to 0.06 \mathrm{~T} in 0.1 \mathrm{~s} find the average emf induced in the coil during this time.(Ans: \left.+1.5 \times 10^{3} \mathrm{~V}\right)
15.3 A coil of wire has 10 loops. Each loop has an area of  1.5 \times 10^{-3} \mathrm{~m}^{2} . A magnetic field is perpendicular to the surface of each loop at all times. If the magnetic field is changed from  0.05 \mathrm{~T}  to  0.06 \mathrm{~T}  in  0.1 \mathrm{~s}  find the average emf induced in the coil during this time.(Ans:  \left.+1.5 \times 10^{3} \mathrm{~V}\right)

15.3 A coil of wire has 10 loops. Each loop has an area of 1.5 \times 10^{-3} \mathrm{~m}^{2} . A magnetic field is perpendicular to the surface of each loop at all times. If the magnetic field is changed from 0.05 \mathrm{~T} to 0.06 \mathrm{~T} in 0.1 \mathrm{~s} find the average emf induced in the coil during this time.(Ans: \left.+1.5 \times 10^{3} \mathrm{~V}\right)

15.5 Two coils are placed side by side. An emf of 0.8 \mathrm{~V} is observed in one coil when the current is changing at the rate of 200 \mathrm{As}^{1} in the other coil. What is the mutual inductance of the coils?(Ans: 4 \mathrm{mH} )
15.5 Two coils are placed side by side. An emf of  0.8 \mathrm{~V}  is observed in one coil when the current is changing at the rate of  200 \mathrm{As}^{1}  in the other coil. What is the mutual inductance of the coils?(Ans:  4 \mathrm{mH}  )

15.5 Two coils are placed side by side. An emf of 0.8 \mathrm{~V} is observed in one coil when the current is changing at the rate of 200 \mathrm{As}^{1} in the other coil. What is the mutual inductance of the coils?(Ans: 4 \mathrm{mH} )

Example 15.3: An emf of 5.6 \mathrm{~V} is induced in a coil while the current in a nearby coil is decreased from 100 \mathrm{~A} to 20 \mathrm{~A} in 0.02 \mathrm{~s} . What is the mutual inductance of the two coils? If the secondary has 200 turns find the change in flux during this interval.
Example 15.3: An emf of  5.6 \mathrm{~V}  is induced in a coil while the current in a nearby coil is decreased from  100 \mathrm{~A}  to  20 \mathrm{~A}  in  0.02 \mathrm{~s} . What is the mutual inductance of the two coils? If the secondary has 200 turns find the change in flux during this interval.

Example 15.3: An emf of 5.6 \mathrm{~V} is induced in a coil while the current in a nearby coil is decreased from 100 \mathrm{~A} to 20 \mathrm{~A} in 0.02 \mathrm{~s} . What is the mutual inductance of the two coils? If the secondary has 200 turns find the change in flux during this interval.

Example 15.7: A permanent magnet D.C motor is run by a battery of 24 volts. The coil of the motor has a resistance of 2 ohms. It develops a back emf of 22.5 volts when driving the load at normal speed. What is the current when motor just starts up? Also find the current when motor is running at normal speed.
Example 15.7: A permanent magnet D.C motor is run by a battery of 24 volts. The coil of the motor has a resistance of 2 ohms. It develops a back emf of  22.5  volts when driving the load at normal speed. What is the current when motor just starts up? Also find the current when motor is running at normal speed.

Example 15.7: A permanent magnet D.C motor is run by a battery of 24 volts. The coil of the motor has a resistance of 2 ohms. It develops a back emf of 22.5 volts when driving the load at normal speed. What is the current when motor just starts up? Also find the current when motor is running at normal speed.

15.4 A circular coil has 15 turns of radius 2 \mathrm{~cm} each. The plane of the coil lies at 40^{\circ} to a uniform magnetic field of 0.2 \mathrm{~T} . If the field is increased by 0.5 \mathrm{~T} in 0.2 \mathrm{~s} find the magnitude of the induced emf.(Ans: 1.8 \times 10^{-2} \mathrm{~V} )
 15.4  A circular coil has 15 turns of radius  2 \mathrm{~cm}  each. The plane of the coil lies at  40^{\circ}  to a uniform magnetic field of  0.2 \mathrm{~T} . If the field is increased by  0.5 \mathrm{~T}  in  0.2 \mathrm{~s}  find the magnitude of the induced emf.(Ans:  1.8 \times 10^{-2} \mathrm{~V}  )
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15.4 A circular coil has 15 turns of radius 2 \mathrm{~cm} each. The plane of the coil lies at 40^{\circ} to a uniform magnetic field of 0.2 \mathrm{~T} . If the field is increased by 0.5 \mathrm{~T} in 0.2 \mathrm{~s} find the magnitude of the induced emf.(Ans: 1.8 \times 10^{-2} \mathrm{~V} )

15.2 A square loop of wire is moving through a uniform magnetic field. The normal to the loop is oriented parallel to the magnetic field. Is a emf induced in the loop? Give a reason for your answer.
15.2 A square loop of wire is moving through a uniform magnetic field. The normal to the loop is oriented parallel to the magnetic field. Is a emf induced in the loop? Give a reason for your answer.
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15.2 A square loop of wire is moving through a uniform magnetic field. The normal to the loop is oriented parallel to the magnetic field. Is a emf induced in the loop? Give a reason for your answer.

15.18 When the primary of a transformer is connected to a.c mains the current in ita) is very small if the secondary circuit is open but
15.18 When the primary of a transformer is connected to a.c mains the current in ita) is very small if the secondary circuit is open but
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15.18 When the primary of a transformer is connected to a.c mains the current in ita) is very small if the secondary circuit is open but

Example 15.8: The turns ratios of a step up transformer is 50. A current of 20 \mathrm{~A} is passed through its primary coil at 220 volts. Obtain the value of the voltage and current in the secondary coil assuming the transformer to be ideal one.
Example 15.8: The turns ratios of a step up transformer is 50. A current of  20 \mathrm{~A}  is passed through its primary coil at 220 volts. Obtain the value of the voltage and current in the secondary coil assuming the transformer to be ideal one.
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Example 15.8: The turns ratios of a step up transformer is 50. A current of 20 \mathrm{~A} is passed through its primary coil at 220 volts. Obtain the value of the voltage and current in the secondary coil assuming the transformer to be ideal one.

Example 15.6: An alternating current generator operating at 50 \mathrm{~Hz} has a coil of 200 turns. The coil has an area of 120 \mathrm{~cm}^{2} . What should be the magnetic field in which the coil rotates in order to produce an emf of maximum value of 240 volts?
Example 15.6: An alternating current generator operating at  50 \mathrm{~Hz}  has a coil of 200 turns. The coil has an area of  120 \mathrm{~cm}^{2} . What should be the magnetic field in which the coil rotates in order to produce an emf of maximum value of 240 volts?
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Example 15.6: An alternating current generator operating at 50 \mathrm{~Hz} has a coil of 200 turns. The coil has an area of 120 \mathrm{~cm}^{2} . What should be the magnetic field in which the coil rotates in order to produce an emf of maximum value of 240 volts?

15.15 A D.C motor operates at 240 \mathrm{~V} and has a resistance of 0.5 \Omega . When the motor is running at normal speed the armature current is 15 \mathrm{~A} . Find the back emf in the armature.(Ans: 232.5V)
 15.15  A D.C motor operates at  240 \mathrm{~V}  and has a resistance of  0.5 \Omega . When the motor is running at normal speed the armature current is  15 \mathrm{~A} . Find the back emf in the armature.(Ans: 232.5V)
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15.15 A D.C motor operates at 240 \mathrm{~V} and has a resistance of 0.5 \Omega . When the motor is running at normal speed the armature current is 15 \mathrm{~A} . Find the back emf in the armature.(Ans: 232.5V)

15.10 Show that \varepsilon and \frac{\Delta \Phi}{\Delta t} have the same units.
 15.10  Show that  \varepsilon  and  \frac{\Delta \Phi}{\Delta t}  have the same units.
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15.10 Show that \varepsilon and \frac{\Delta \Phi}{\Delta t} have the same units.

15.9 In a certain region the earths magnetic field point vertically down. When a plane flies due north which wingtip is positively charged?
 15.9 In a certain region the earths magnetic field point vertically down. When a plane flies due north which wingtip is positively charged?
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15.9 In a certain region the earths magnetic field point vertically down. When a plane flies due north which wingtip is positively charged?

15.4 What is the direction of the current through resistor R in Fig.Q.15.4?. When switch S is(a) closed(b) opened.Fig. Q. 15.4
 15.4  What is the direction of the current through resistor  R  in Fig.Q.15.4?. When switch S is(a) closed(b) opened.Fig. Q.  15.4
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15.4 What is the direction of the current through resistor R in Fig.Q.15.4?. When switch S is(a) closed(b) opened.Fig. Q. 15.4

15.18 An ideal step down transformer is connected to main supply of 240 \mathrm{~V} . It is desired to operate a 12 \mathrm{~V} 30 \mathrm{~W} lamp. Find the current in the primary and the transformation ratio?(Ans: 0.125A 1/20)
15.18 An ideal step down transformer is connected to main supply of  240 \mathrm{~V} . It is desired to operate a  12 \mathrm{~V} 30 \mathrm{~W}  lamp. Find the current in the primary and the transformation ratio?(Ans: 0.125A 1/20)
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15.18 An ideal step down transformer is connected to main supply of 240 \mathrm{~V} . It is desired to operate a 12 \mathrm{~V} 30 \mathrm{~W} lamp. Find the current in the primary and the transformation ratio?(Ans: 0.125A 1/20)

15.9 When current through a coil changes from 100 \mathrm{~mA} to 200 \mathrm{~mA} in 0.005 \mathrm{~s} an induced emf of 40 \mathrm{mV} is produced in the coil. (a)What is the self inductance of the coil?(b) Find the increase in the energy stored in the coil.(Ans: 2 \mathrm{mH} 0.03 \mathrm{~mJ} )
 15.9  When current through a coil changes from  100 \mathrm{~mA}  to  200 \mathrm{~mA}  in  0.005 \mathrm{~s}  an induced emf of  40 \mathrm{mV}  is produced in the coil. (a)What is the self inductance of the coil?(b) Find the increase in the energy stored in the coil.(Ans:  2 \mathrm{mH} 0.03 \mathrm{~mJ}  )
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15.9 When current through a coil changes from 100 \mathrm{~mA} to 200 \mathrm{~mA} in 0.005 \mathrm{~s} an induced emf of 40 \mathrm{mV} is produced in the coil. (a)What is the self inductance of the coil?(b) Find the increase in the energy stored in the coil.(Ans: 2 \mathrm{mH} 0.03 \mathrm{~mJ} )