Question

A horizontal straight metallic rod of length 4 m is held at some height above the surface of Earth, in east-west direction. If it is allowed to fall from rest, find the : (a) emf induced in the rod 2 s after it starts falling, (b) polarity of the emf induced, and (c) the end of the rod which is at the higher potential. The horizontal component of the Earth's magnetic field at the place is 0·3 × 10⁻⁴ Wb/m² and take g = 10 m/s².

A rod PQ of resistance R lies across frictionless conducting rails in a constant uniform magnetic field B, as shown in the figure. Assuming that the rails have negligible resistance, the force required to pull the rod to the right at constant velocity v is:

The figure shows a rectangular conductor PQRS in which the arm PQ of length 10 cm and resistance 0.4 Ω is free to move. It is kept in a uniform magnetic field B = 0.2 T acting perpendicular into the plane of PQRS. If arm PQ is moved with a velocity v of 5 cm/s as shown, find : (a) the current induced in the loop, and (b) the power required to move the arm. (Resistances of arms PS, SR and RQ are negligible.)

A rectangular conductor MNPQ with a movable arm MN (resistance r) is kept in a uniform magnetic field as shown in the figure. Resistance of arms MQ, QP and PN are negligible. Obtain the expression for the : (a) current induced in the loop specifying its direction, and (b) power required to move the arm.