Three point charges

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

Three point charges, each

q = +2.5\,\mathrm{nC}

, are held at rest in vacuum at the corners of an equilateral triangle of side

a = 0.15\,\mathrm{m}

lying in the

xy

-plane. The centroid of the triangle is at the origin, and each corner is a distance

R = a/\sqrt{3}

from the centroid. No other charges are present and

V = 0

at infinity. Use

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

. ((a)) Find the potential at the centroid by adding the potentials of the three charges. ((b)) Every corner is a distance

\sqrt{R^2+z^2}

from the point

(0,0,z)

on the axis through the centroid, so on that axis

V(z) = \frac{1}{4\pi\varepsilon_0}\,\frac{3q}{\sqrt{R^2+z^2}}.

Differentiate this to obtain the

z

-component of the field, evaluate it at

z = 0.20\,\mathrm{m}

and state its direction. ((c)) Find the electrostatic potential energy of this arrangement of three charges, i.e. the work needed to assemble it from charges initially far apart.

Browse the problem library