Electricity and Magnetism

9–66 Electricity and Magnetism

V (P) =

N

X

i=1

V

i

(P) =

N

X

i=1

k ∆q

i

|~r

i

|

i

P

+

~r

i

FIGURE 9.4 Obtaining the Electrostatic Potential outside a Distribution of Charge

Electrostatic Potential Energy and Distributions of Charge

As has become customary, the partition, compute, and sum method is employed to deal

with continuous distributions of charge. The distributed charge is partitioned into N small

charge elements, ∆q

i

, as shown in Figure 9.4. The contribution to the potential at the field

point P due to each charge element, treated as a point charge, is computed. These are

summed to yield the net potential at P.

Infinitely refining the partition, via the simultaneous ...