Question

There are two frictionless conducting rails placed in a transverse uniform magnetic field $B$ as shown in the figure. The rails are connected by a fixed capacitive arm $AB$ and a movable conducting rod $PQ$ is also placed as shown. If the rod $PQ$ is given a rightward initial velocity $V$ then the graph that best represents variation of speed of rod as a function of time

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

The equivalent circuit is,

$\frac{q}{C}=BLV$( Emf generated due to moving rod$=BLV$)
$q=BLVC$
Differentiating the above equation
$i=BLCa$
Force on the rod,
$F=-BiL$
$ma=-B^2{L}^{2}Ca$
$a(m+b^2{L}^{2}C)=0$
As $(m+b^2{L}^{2}C)\ne 0$ then $\Rightarrow a=0$
Thus $V$ is constant.