Question

A parallel plate capacitor with plate area A and separation between the plates d, is charged by a current l Displacement current through a plane surface of area $A/2$ parallel to the plates and drawn symmetric between the plates, is

• A. l
• B. $\frac{5l}{4}$
• C. $\frac{l}{4}$
• D. $\frac{3l}{2}$

Answer 1

The correct option is C $\frac{l}{4}$

$\begin{array}{c}Ifqbethecheonthecapacitorattime{t}_1,thenelectricfiledbetweenplatesofthecpaacitor,\\ E=\frac{q}{{\in }_{0}A}\\ Fluxthroughthearea,\varphi E=\left(\frac{q}{{\in }_{0}A}\right)\left(\frac{A}{4}\right)=\frac{q}{4{\in }_0}\\ Displacementcurrent{I}_D={\in }_0\frac{d\varphi E}{dt}={\in }_0\frac{d\left(\frac{q}{4}{\in }_0\right)}{dt}=\frac{1}{4}\frac{dq}{dt}=\frac{i}{4}\\ Hence,theanswerBisthecorrectanswer.\end{array}$