Question

A dielectric slab of area $A$ and thickness $d$ is inserted between the plates of a capacitor of area $2A$ with constant speed $v$ as shown in the figure. Distance between the plates is $d$.

The capacitor is connected to a battery of e.m.f. $E$; the current in the circuit varies with time as

• A.
• B.
• C.
• D. none of these

Answer 1

The correct option is B

There are three cases
Case-I : Inserting dielectric

$Q=CV$ and after time t,
$Q=[\frac{K{\epsilon }_0(v\times t)\times d}{d}+\frac{{\epsilon }_0(2A-(v\times t\times d\left)\right)}{d}]\times E$
On differentiating
$\frac{dQ}{dt}=i=[\frac{K{\epsilon }_{0}vd}{d}-\frac{{\epsilon }_{0}v\times d}{d}]E$
$i=[K{\epsilon }_{0}v-{\epsilon }_{0}v]E$

Case-II : The moment dielectric is completely inside

$C=\frac{K{\epsilon }_{0}A}{d};Q=CV$
$Q=\frac{K{\epsilon }_{0}A}{d}E$
$\frac{dQ}{dt}=0$

Case-III : Dielectric coming out

The capacitor will charge the battery as potential is changing with the same current in reverse direction.