Question

The area of the plates of a capacitor is $10c{m}^2$ each and the separation between them is 10 mm. The surface charge density of each facing side is $100\mu C/c{m}^2$. The energy stored inside the capacitor is?

• A. $4.6\times {10}^{5}J$
• B. $5.6\times {10}^{5}J$
• C. $3.6\times {10}^{5}J$
• D. None of these

Answer 1

The correct option is B $5.6\times {10}^{5}J$

First let’s see if we can find the capacitance from the data given
$C=\frac{\epsilon A}{d}$
A and d are given. Permittivity of free space will be taken since no dielectric medium is mentioned.
$C=\frac{8.854\times {10}^{-12}\times {10}^{-3}}{{10}^{-2}}$
$C=8.854\times {10}^{-13}$
Now energy is
$E=\frac{1}{2}C{V}^2$
We’re given the charge instead of V,
So if we replace $V=\frac{Q}{C}$ for the energy equation, it becomes
$E=\frac{1}{2}\frac{Q^2}{C}Q=100\times \frac{{10}^{-6}}{{10}^{-4}}\times {10}^{-3}Q=1mCSo,E=\frac{1}{2}\frac{{10}^{-3\times 2}}{8.854\times {10}^{-13}}E=5.6\times {10}^{5}J$