Question

A parallel plate condenser has a uniform electric field $E\, (V/m)$ in the space between the plates. If the distance between the plates is $d\, (m)$ and area of each plate is $A \,(m^2)$ the energy (joules) stored in the condenser is :

• A. $\frac{1}{2} \in_0 E^2 Ad$
• B. $E^2 Ad \in_0 $
• C. $\frac{1}{2} \in_0 E^2 $
• D. $ \in_0 E Ad$

Answer 1

Answer: (A)

$U =\frac{1}{2} \,CV ^{2}$
$=\frac{1}{2}\left(\frac{\in_{0}\, A }{ d }\right) V ^{2}$
$=\frac{1}{2}\left(\epsilon_{0}\, Ad \right)\left(\frac{ V }{ d }\right)^{2}=\frac{1}{2} \in_{0} \,E ^{2} \,Ad$