A long duct of square cross-section has walls

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

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

Problem

x=0

x=a

and

y=0

earthed, with

a = 0.20\,\mathrm{m}

. The fourth wall,

y=a

, is held at

V(x,a) = V_0\sin(2\pi x/a), \qquad V_0 = 50\,\mathrm{V}.

Thin insulating gaps separate the live wall from its earthed neighbours. Find the potential at the interior point

(a/4,\,a/2)

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