91Ó°ÊÓ

The energy density is defined as the energy per unit volume. For an electric field, it depends only on the magnitude of electric field strength.

The energy density in an electric field is given as:

\(u = \frac{1}{2}{\varepsilon _0}{E^2}\) … (i)

Here,\({\varepsilon _0}\)is the permittivity of free space and E is the electric field strength.

The electric field strength is, \(E = 150\;{\rm{V/m}}\)

The energy stored per cubic meter in the field is calculated as:

\(\begin{aligned}{c}U &= \frac{1}{2}{\varepsilon _0}{E^2}\\ &= \frac{1}{2}\left( {8.854 \times {{10}^{ - 12}}\;{{\rm{C}}^{\rm{2}}}{\rm{/N}} \cdot {{\rm{m}}^{\rm{2}}}} \right){\left( {150\;{\rm{V/m}}} \right)^2}\\ &= 9.96 \times {10^{ - 8}}\;{\rm{J/}}{{\rm{m}}^{\rm{3}}}\\ \approx 1.0 \times {10^{ - 7}}\;{\rm{J/}}{{\rm{m}}^{\rm{3}}}\end{aligned}\)

Thus, the energy stored per cubic meter in the field is \(1.0 \times {10^{ - 7}}\;{\rm{J/}}{{\rm{m}}^{\rm{3}}}\).