Question

A square metal loop of side $10cm$ and resistance $1\Omega$ is moved with a constant velocity partly inside a uniform magnetic field of $2Wb{m}^{-2}$, directed into the paper, as shown in the figure. The loop is connected to a network of five resistors each of value $3\Omega$. If a steady current of $1mA$ flows in the loop, then the speed of the loop is

• A. $0.5cm{s}^{-1}$
• B. $1cm{s}^{-1}$
• C. $2cm{s}^{-1}$
• D. $4cm{s}^{-1}$

Answer 1

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

$\epsilon =Blv=2\times {10}^{-1}\times v=0.2v$

$I=\frac{\epsilon }{R}={10}^{-3}\Rightarrow \frac{0.2v}{4}={10}^{-3}$

[Since effective resistance R of bridge is $R=\frac{6\times 6}{6+6}=3\Omega$

so total resistance $=1+3=4\Omega$]
$\Rightarrow v=2cm{s}^{-1}$