Physics 230 March 20 2002

Find the electric energy density at point P as shown in the diagram.

The electric energy density is

u = (epsilon0)E2/2
First we find the electric field at P.  This is the sum of the two electric fields produced by each of the two charges.  Each has the same magnitude, since each charge has the same magnitude and is the same distance from P.  The vectors also make equal angles with the perpendicular bisector of the line between the charges, as shown in the diagram.  Thus the horizontal components add to zero, and the vertical component is
Ey = 2kqd/(l2 + d2 )3/2
Thus the energy density is:
u = 2(epsilon0)(kqd)2/(l2 + d2 )3
=(k/2pi)(qd)2/(l2 + d2 )3