Physics Class 12 NCERT Solutions: Chapter 6 Electromagnetic Induction Part 3

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Self inductance formula

Self Inductance Formula

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Q: 6. A circular coil of radius and turns is rotated about its vertical diameter with an angular speed of in a uniform horizontal magnetic field of magnitude . Obtain the maximum and average emf induced in the coil. If the coil forms a closed loop of resistance , calculate the maximum value of current in the coil. Calculate the average power loss due to Joule heating. Where does this power come from?

Answer:

Maximum induced emf

Average induced emf

Maximum current in the coil

Average power loss

(Power comes from the external rotor)

Radius of the circular coil,

Area of the coil,

Number of turns on the coil,

Angular speed,

Magnetic field strength,

Resistance of the loop,

The maximum emf induced in the coil is 0.603 V.

Over a full cycle, the average emf induced in the coil is zero.

Maximum current is given as:

Average power loss due to joule heating:

The current induced in the coil produces a torque opposing the rotation of the coil. The rotor is an external agent. It must supply a torque to counter this torque in order to keep the coil rotating uniformly. Hence, dissipated power comes from the external rotor.

Q: 7. A horizontal straight wire long extending from east to west is falling with a speed of , at right angle to the horizontal component of the earth’s magnetic field, .

(A) What is the instantaneous value of the emf induced in the wire?

(B) What is the direction of the emf?

(C) Which end of the wire is at the higher electrical potential?

Answer:

Length of the wire,

Falling speed of the wire,

Magnetic field strength,

(A) Emf induced in the wire,

(B) Using Fleming’s right hand rule, it can be inferred that the direction of the induced emf is from west to East.

(C) The eastern end of the wire is at a higher potential.

Q: 8. Current in a circuit falls from in. If an average emf of induced give an estimate of the self –inductance of the circuit.

Answer:

Initial current,

Final current,

Change in current,

Time taken for

Average emf,

For self-inductance (L) of the coil, we have the relation for average emf as:

Hence, the self-induction of the coil is .