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 resistance 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. 6 N
• B. 4 N
• C. 2 N
• D. 1 N

Answer 1

The correct option is C 2 N

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



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