Sol . E = – ∇ ∇ V= –

= – 2a x – 4a y (V/m)

This field is constant in magnitude (E = V/m) and direction over all space, and so the total stored energy is infinite. (The field could be that within an infinite parallel-plate capacitor. It would take an infinite amount of work to charge such a capacitor.)

Nevertheless, it is possible to speak of an energy density for this and other fields. The expression

W E = dv

suggests that each tiny volume dv be assigned the energy content wdv, where

w =

For the present field, the energy density is constant:

w = (20) = J/m 3 and so every 1-m

3 volume contains (10 –8 /36π) J of energy.