Two point charges are held at rest on the -axis in vacuum: at the origin and at

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electrostatic fields and potential · Electrostatic fields and potential

Electricity, Magnetism and Electromagnetism, Ch Electrostatic potential, potential energy and the energy of the field

Problem

Two point charges are held at rest on the

x

-axis in vacuum:

q_1 = +4.0\,\mathrm{nC}

at the origin and

q_2 = -2.0\,\mathrm{nC}

x = d = 0.30\,\mathrm{m}

. No other charges are present anywhere. Take

V = 0

at infinity, and let

P

be the point

x = 0.10\,\mathrm{m}

on the axis. Use

1/4\pi\varepsilon_0 = 8.99\times10^{9}\,\mathrm{N\,m^2\,C^{-2}}

. ((a)) Find the potential at

P

by adding the potentials of the two charges as numbers. ((b)) For a point of the axis with

0 < x < d

the potential of this pair is

V(x) = \frac{1}{4\pi\varepsilon_0}\left(\frac{q_1}{x} + \frac{q_2}{d-x}\right).

Differentiate this to obtain the

x

-component of the electric field, evaluate it at

P

and state its direction. ((c)) A third charge

q_3 = +3.0\,\mathrm{nC}

is now brought in slowly from infinity and held at

P

. Find the total electrostatic potential energy of the three charges.

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