A point charge sits at one corner of a cube of side

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

Mathematical Methods for Physics, Ch The integral theorems: Gauss, Stokes and Green

Problem

A point charge

q = 1.0\,\mathrm{nC}

sits at one corner of a cube of side

L

, with nothing else nearby. Take

\epsilon_0 = 8.854\times10^{-12}\,\mathrm{F\,m^{-1}}

. ((a)) Explain why the three faces that meet at the charge's corner carry no flux, and why neither the divergence theorem nor Gauss's law can be applied to this cube as it stands. ((b)) Find the flux of

\mathbf{E}

out through each of the other three faces, and the total flux out of the cube. ((c)) Suppose, hypothetically, that the field of a point charge were radial with

E_r = C/r^{2.1}

for a constant

C

, instead of falling off as

1/r^2

. Would the flux out through a sphere centred on the charge still be the same at every radius? Decide from the divergence of this field, not by integrating over a sphere.

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