question_answer

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 = 2W. Two resistance of 6W and 3W 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

Correct Answer: C

Solution :

                   Motional emf \[e=Bvl\Rightarrow e=2\times 2\times 1=4\ V\] This acts as a cell of emf \[E=4\ V\]and internal resistance \[r=2\Omega \]. This simple circuit can be drawn as follows Current through the connector \[i=\frac{4}{2+2}=1\ A\] \magnetic force on connector\[{{F}_{m}}=Bil=2\times 1\times 1=2\ N\] (Towards left)