A duct has cross-section

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Electricity, Magnetism & Electromagnetism · Conductors, capacitance and boundary-value electrostatics

The Boundary-Value Problem, Ch Separation of variables in Cartesian geometry

Problem

0<x<a

0<y<b

with

a=0.40\,\mathrm{m}

b=0.20\,\mathrm{m}

. Walls

x=0

x=a

y=0

are earthed; the wall

y=b

is held at

V_0=60\,\mathrm{V}

, with thin insulating gaps at the corners. Find the potential at

(3a/4,\,b/2)

to within

1\,\mathrm{V}

, stating how many non-zero terms are needed.

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