Answer to Question #248639 in Electricity and Magnetism for Mosses07

Question

Particle A carrying a charge of 9.0 nC is at the origin of a Cartesian coordinate system.

(a) What is the electrostatic potential (relative to zero potential at infinity) at a position r = 4.0 m from the origin?

(b) With particle A held in place at the origin, how much work must be done by an outside agent to bring particle B, also carrying a 9.0-nC charge, from infinity to r = 4.0 m?

(c) Particle B is returned to infinity, and particle A is moved to r = 4.0 m and held there. How much work must be done by an outside agent to bring particle B from infinity to the origin?

Answer 1

a) The potential 4 m from the origin is

$$V=\frac{kq}{r}=20.2\text{ V}.$$

b) The potential of particle A in infinity is infinitesimal, or zero (speaking mathematically), so, the work equals charge B times potential difference:

$$W=q_B\Delta V=1.82·10^{-7}\text{ J}.$$

c) The work is the same like in (b) as it is defined by the initial and final potential.