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 conector 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=2 m/s is

• A. 6 N
• B. 4 N
• C. 2 N
• D. 1 N

Answer 1

The correct option is C 2 N

$\begin{array}{cc}F=Bil=B\frac{E}{R^{\prime }}l& R^1=\frac{6\times 3}{6+3}+2\\ =B\left[\frac{Blv}{R^{\prime }}\right]l& =2+2\\ F=\frac{B^2{l}^{2}v}{R^1}& R^1=4\Omega \\ =\frac{2^2\times 1^2\times 2}{4}& \end{array}$

$F=2N$