Electricity and Magnetism

Chapter 9

Electrostatic Potential Energy

Example [ Electric Potential Associated with an Isolated Point Charge ]

An isolated point charge, q, lies at the origin of coordinates. Two field points lie at ~r

1

and

~r

2

, respectively. The electric potential difference between these points, ∆V

12

, is

∆V

12

= V (~r

2

) − V (~r

1

) = −

Z

~r

2

~r

1

→

E

q

· d~s .

The electric field produced by the isolated point charge is directed radially outward, with

its magnitude falling off as the square of the distance from the charge,

→

E

q

=

k q

r

2

ˆr .

Accordingly, only the radial components of the path survive the projection onto the field in

the integrand.

ASIDE: The equipotential sur faces in this ...