91Ó°ÊÓ

A capacitor is a charge and energy storage device. The stored energy is proportional to the square of the magnitude of the charge on the plates.

The expression for stored energy in the capacitor is given as:

\({\rm{PE}} = \frac{{{Q^2}}}{{2C}}\) … (i)

Here, C is the capacitance and Q is the charge on the capacitor plates.

The side of the square plates is,\(s = 8.0\;{\rm{cm}} = 0.08\;{\rm{m}}\).

The separation of the plates is,\(d = 1.5\;{\rm{mm}} = 1.5 \times {10^{ - 3}}\;{\rm{m}}\).

The magnitude of the charge on the plates is, \(Q = 370\;\mu {\rm{C}} = 370 \times {10^{ - 6}}\;{\rm{C}}\).

The area of the square plate is,

\(A = {s^2}\)

The capacitance of the capacitor is given as:

\(\begin{aligned}{l}C = {\varepsilon _0}\frac{A}{d}\\C = {\varepsilon _0}\frac{{{s^2}}}{d}\end{aligned}\)

Substitute the values in the above expression.

\(\begin{aligned}{c}C &= \left( {8.854 \times {{10}^{ - 12}}\;{{\rm{C}}^{\rm{2}}}{\rm{/N}} \cdot {{\rm{m}}^{\rm{2}}}} \right)\frac{{{{\left( {0.08\;{\rm{m}}} \right)}^2}}}{{\left( {1.5 \times {{10}^{ - 3}}\;{\rm{m}}} \right)}}\\C &= 3.78 \times {10^{ - 11}}\;{\rm{F}}\end{aligned}\)

The energy stored in the capacitor is given as:

\({\rm{PE}} = \frac{{{Q^2}}}{{2C}}\)

Substitute the values in the above expression.

\(\begin{aligned}{c}{\rm{PE}} &= \frac{{{{\left( {370 \times {{10}^{ - 6}}\;{\rm{C}}} \right)}^2}}}{{2 \times 3.78 \times {{10}^{ - 11}}\;{\rm{F}}}}\\ &= 1.8 \times {10^3}\;{\rm{J}}\end{aligned}\)

Thus, the energy stored by the electric field between two square plates is \(1.8 \times {10^3}\;{\rm{J}}\).