Question

Josh stored an electric potential energy of 2.5j in a vacuum of 1.00m3 by a field E. If the field is reduced to 0.25 of its initial value, how much energy is stored per cubic meter?

Answer 1

we know that ,

electric potential energy in a volume is given by:

(energy density) $\times$ (volume) = $({1\over2} \epsilon_0 E^2)\times(volume)$

here,

P.E.=2.5 J= $({1\over2} \epsilon_0 E^2)\times(1)$

now we reduced E by 0.25 times ,

now new potential energy will be,

P.E.= $({1\over2} \epsilon_0({ E\over4})^2)\times(1)$

=$2.5\over16$ J

=0.156 J