question_answer

Two identical capacitors having plate separation \[{{d}_{0}}\] are connected parallel to each other across points A and B as shown in figure. A charge Q is imparted to the system by connecting a battery across A and B and battery is removed. Now first plate of first capacitor and second plate of second capacitor starts moving with constant velocity \[{{u}_{0}}\]towards left. Find the magnitude of current flowing in the loop during the process.

A) \[\frac{Q}{2{{d}_{0}}}{{u}_{0}}\]

B)                    \[\frac{Q}{{{d}_{0}}}{{u}_{0}}\]

C) \[\frac{2Q}{{{d}_{0}}}{{u}_{0}}\]      

D)        \[\frac{Q}{3{{d}_{0}}}{{u}_{0}}\]

Correct Answer: A

Solution :

Let each plate moves a distance x from its initial position. Let q charge flows in the loop. Using Kirchoff?s voltage law \[\frac{\left( \frac{Q}{2}-q \right)\,({{d}_{0}}+x)}{{{\in }_{0}}A}-\frac{\left( \frac{Q}{2}+q \right)({{d}_{0}}-x)}{{{\in }_{0}}A}=0\] \[\therefore \,\,q=\frac{Qx}{2{{d}_{0}}};\] \[I=\frac{dq}{dt}=\frac{Q}{2{{d}_{0}}}\left( \frac{dx}{dt} \right)=\frac{Q}{2{{d}_{0}}}{{u}_{0}}\]