Question

A rectangular loop with a sliding connector of length l = 1.0 m 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 is

• A. 6N
• B. 4N
• C. 2N
• D. 1N

Answer 1

The correct option is C 2N

Motional emf $e=Bvl\Rightarrow e=2\times 2\times 1=4$ V
This acts as a cell of emf E=4V and internal resistance r=2$\Omega$.
This simple circuit can be drwan as follows



Current through the connector $i=\frac{4}{2+2}=$1 A
$\therefore$ Magnetic force on connector $F_m=$=Bil=$2\times 1\times 1=2$ N (Towards left)