Question

A square metal wire loop of side 10 cm and resistance $$1 \Omega$$ is moved with constant velocity $$v_0$$ in a uniform magnetic field of induction $$B = 2 Wbm^{-2} ,$$ as shown in Fig. 6.3. The magnetic field lines are perpendicular to the plane of loop and directed into the paper. The loop is connected to the network of resistances, each of value $$3 \Omega.$$ The resistance of the lead wire is negligible. The speed of the loop so as to have a steady current of $$1 \,mA$$ in the loop is

Answer 1

Correct option is B. $$2 \,cms^{-1}$$
Effective resistance of circuit is $$4$$ $$\Omega$$

$$I$$ = $$\dfrac{E}{R}$$ = $$\dfrac{Blv}{R}$$ or $$v$$ = $$\dfrac{IR}{Bl}$$

or $$v$$ = $$\dfrac{1\times 0.001\times4}{2\times 10\times0.01} m s^{-1}$$ = $$0.02m s^{-1}$$ = $$2 cm s^{-1}$$