Question

A square metal wire loop of side $10cm$ and resistances $1\Omega$ is moved with constant velocity $v_0$ in a uniform magnetic field of induction $B=2Wb$ $m^{-2}$, as shown in figure. 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 wires is negligible. The speed of the loop so as to have a steady current of $1mA$ in the loop is

• A. $2m$ $s^{-1}$
• B. $2cm$ $s^{-1}$
• C. $10m$ $s^{-1}$
• D. $20m$ $s^{-1}$

Answer 1

The correct option is B $2cm$ $s^{-1}$

Magnetic Flux, $\varphi =BLx$
Induced EMF, $E=\frac{d\varphi }{dt}=BL{v}_o$
Total resistance of the loop, $R=1\Omega +3\Omega =4\Omega$
(Using wheatstone bridge theory)
$i=\frac{V}{R}$
${10}^{-3}=\frac{BL{v}_o}{4}$
$v_o=0.02m/s$