# NCERT Physics Class 12 Exemplar Ch 6 Electromagnetic Inductions Part 5

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Q 26. A rectangular loop of wire ABCD is kept close to an infinitely long wire carrying a current for and Find the total charge passing through a given point in the loop, in time T. The resistance of the loop is R.

If is the current in the loop.

If Q is the charge that passed in time t,

Integrating

The magnitude of change is

Q.27 A magnetic field B is confined to a region and points out of the paper (the z-axis), being the centre of the circular region. A charged ring (charge) of radius and mass m lies in the plane with its centre at the origin. The ring is free to rotate and is at rest. The magnetic field is brought to zero in time. Find the angular velocity of the ring after the field vanishes.

Ans:

Torque

If is the change in angular momentum

Initial angular momentum

Final angular momentum

Q 28. A rod of mass m and resistance R slides smoothly over two parallel perfectly conducting wires kept sloping at an angle with respect to the horizontal. The circuit is closed through a perfect conductor at the top. There is a constant magnetic field B along the vertical direction. If the rod is initially at rest, find the velocity of the rod as a function of time.

Ans:

(A is a constant to be determine by initial conditions)

Q 29. Find the current in the sliding rod AB (resistance = R) for the arrangement shown in. B is constant and is out of the paper. Parallel wires have no resistance. v is constant. Switch S is closed at time.

Ans:

If Q (t) is charge on the capacitor (note current flows from A to B)

. Differentiating, we get