Two equal point charges are held at rest in vacuum at and

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 equal point charges

q = +6.0\,\mathrm{nC}

are held at rest in vacuum at

(x,y) = (+0.15\,\mathrm{m}, 0)

and

(-0.15\,\mathrm{m}, 0)

, so

a = 0.15\,\mathrm{m}

. No other charges are present. Take

V = 0

at infinity, and let

P

be the point

(0, 0.20\,\mathrm{m})

on the

y

-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. ((b)) On the

y

-axis the potential of the pair is

V(y) = \frac{1}{4\pi\varepsilon_0}\,\frac{2q}{\sqrt{a^2+y^2}}.

Differentiate this to obtain the

y

-component of the electric field, evaluate it at

P

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

q_3 = -4.0\,\mathrm{nC}

is brought in slowly from infinity and held at

P

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

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