Question

A rectangular loop with a sliding connector of length $l=1.0m$ is situated in a uniform magnetic field $B=2T$ perpendicular to the plane of loop. Resistance of connector is $r=2\Omega$. Two resistances of $6\Omega$ and $3\Omega$ are connected as shown in figure. The external force required to keep the connector moving with a constant velocity $v=2m{s}^{-1}$ is

• A. $6N$
• B. $4N$
• C. $2N$
• D. $1N$
• E. $0N$

Answer 1

Answer: (C)

$2N$

$6\Omega and3\Omega reisistorsareinparallelandequivalentreisistanceis2\Omega +2\Omega =4\Omega .$
$F=Bil=BL\frac{BLv}{R_{eq}}$
$=\frac{B^2{l}^{2}v}{R_{eq}}=\frac{2^2\times 1^2\times 2}{4}=2N$