A long square duct of side 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

A long square duct of side a=0.25 ma=0.25\,\mathrm{m} has walls x=0x=0, x=ax=a, y=0y=0 earthed. The wall y=ay=a is held at V(x,a)=V0sin⁡(4πx/a),V0=90 V.V(x,a)=V_0\sin(4\pi x/a),\qquad V_0=90\,\mathrm{V}. Find the potential at (a/3, a/2)(a/3,\,a/2).

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