Physics Class 12 NCERT Solutions: Chapter 6 Electromagnetic Induction Part 2

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Flux approch to motional emg in a wire

Flux Approch to Motional Emf in a Wire

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Q: 3. A long solenoid with turns per has a small loop of area placed inside the solenoid normal to its axis. If the current by the solenoid changes steadily from in, what is the induced emf in the in the loop while the loop while the current is changing?


Number of turns on the solenoid

Number of turns per unit length,

The solenoid has a small loop of area,

Current carried by the solenoid changes from.

Change in current in the solenoid,

Change in time,

Induced emf in the solenoid is given by faraday’s law as:


Induced flux through the small loop

Permeability of free space

Hence, equation (i) reduces to:

Hence, the induced voltage in the loop is.

Q: 4. A rectangular wire loop of sides and with a small cut is moving out of a region of uniform magnetic field of magnitude 0.3 T directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is in a direction normal to the (a) longer side, (b) shorter side of the loop? For how long does the induced voltage last in each case?

Answer: Length of the rectangular wire,

Width of the rectangular wire,

Hence, area of the rectangular loop,

Magnetic field strength,

Velocity of the loop,

(A) Emf developed in the loop is given as:

Time taken to travel along the width,

Hence, the induced voltage is which lasts for s.

(b) Emf developed,

Time taken to travel along the length,

Hence, the induced voltage is which lasts for s.

Q: 5. A long metallic rod is rotated with an angular frequency of rad about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field of parallel to the axis exists everywhere. Calculate the emf developed between the centre and the ring.


Length of the rod,

Angular frequency,

Magnetic field strength,

One end of the rod has zero linear velocity, while the other end has a linear velocity of.

Average linear velocity of the rod,

Emf developed between the centre and the ring,

Hence, the emf developed between the centre and the ring is 100 V.