Question

A square metal loop of side $10$ cm and resistance $1\Omega$ is moved with a constant velocity partly inside a uniform magnetic field of $2 Wbm^{-2}$, directed into the paper, as shown in the figure.

Answer 1

$\varepsilon = B\ell v = 2 \times10^{-1} \times v =0.2v$
$I = \frac{\varepsilon}{R} =10^{-3}$
$\Rightarrow \frac{0.2v}{4} = 10^{-3}$
[Since effective resistance $R$ of bridge is $R = \frac{6 \times6}{6 +6} = 3\Omega$
so total resistance $= 1 +3 =4\Omega$]
$\Rightarrow v =2cm \,s^{-1}$