Question

A square metal wire loop of side 10 cm and of resistance 2 $\Omega$ moves with constant velocity in the presence of a uniform magnetic field of induction 4 T, perpendicular and into the plane of the loop. The loop is connected to a network of resistance as shown in the Figure. If the loop should have a steady current of 2 mA, the speed of the loop must be (in cm s${}^{-1}$) :

• A. $4$
• B. $2$
• C. $3$
• D. $6$

Answer 1

The correct option is B $2$

As this is wheatstore bridge.

$R_{eq}=\frac{6\times 3}{6+3}=2\Omega$

$Totalresistance=2+2=4\Omega$
Now steady current is 2mA
$\therefore$ Voltage required $=\left(.002\right)4$
$=0.008V=8mV$
$B=4T$

$E=8mV=\frac{-d\varphi }{dt}$$=\frac{-d4\left(Area\right)}{dt}$

$8\times {10}^{-3}=4\times \left(0.10\right)V$
$V=2\times {10}^{-2}m/s$
$=2cm/s$