Question

A parallel plate capacitor is connected to a battery of emf $10\text{V}$. If the separation between the two plates is $5\text{mm}$, then the energy stored per unit volume between the plates is

• A. $17.7\mu {\text{J/m}}^3$
• B. $17.7{\text{J/m}}^3$
• C. $1.77\times {10}^{-4}{\text{J/m}}^3$
• D. $1.77\mu \text{J}/{\text{m}}^3$

Answer 1

The correct option is A $17.7\mu {\text{J/m}}^3$

Energy stored per unit volume is the energy density$\left(u\right)$

$u=\frac{1}{2}{ϵ}_0{E}^2$

For the uniform electric field existing between the plates of a parallel plate capacitor we can use,

$E=\frac{V}{d}$


On substituting the value we get,

$\Rightarrow u=\frac{1}{2}{ϵ}_0\frac{V^2}{d^2}$

$u=\frac{1}{2}\times \frac{8.85\times {10}^{-12}\times 10\times 10}{5\times 5\times {10}^{-6}}{\text{J/m}}^3$

$\Rightarrow u=1.77\times {10}^{-5}{\text{J/m}}^3$

$\therefore u=17.7\mu {\text{J/m}}^3$