Two infinite

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electrostatic fields and potential · Conductors, capacitance and boundary-value electrostatics

The Boundary-Value Problem, Ch Uniqueness, images and the Green function of a region

Problem

Two infinite, earthed, perfectly conducting planes meet at a right angle, occupying

x=0

(for

y\ge0

) and

y=0

(for

x\ge0

), so that the vacuum region

x>0,\ y>0

is bounded by the two planes and is otherwise empty of charge. A point charge

q

sits in this region at

(x_0,y_0)

. ((a)) Give the positions and magnitudes of the image charges needed so that

V=0

on both planes, and say why no further image is required. ((b)) Take

q=2.0\,\mathrm{nC}

x_0=3.0\,\mathrm{cm}

(the distance from

q

to the plane

x=0

) and

y_0=4.0\,\mathrm{cm}

(the distance from

q

to the plane

y=0

). Find the

x

- and

y

-components of the net force on

q

, and its magnitude.

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