A thin spherical shell of radius is held at the potential V( , ) = V_1 + V_0 on r = a

PHYSICS · Multi-part · 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 spherical geometry

Problem

A thin spherical shell of radius

a = 0.20\,\text{m}

is held at the potential

V(\theta,\phi) = V_1 + V_0\sin\theta\sin\phi \qquad \text{on } r = a,

with

V_1 = 45\,\text{V}

and

V_0 = 150\,\text{V}

. The potential is zero at infinity. Find the potential inside and outside the shell (as functions of

r

\theta

\phi

), and use it to answer: ((a)) What is the potential at the point

r = 0.10\,\text{m}

\theta = 90^\circ

\phi = 90^\circ

(inside the shell, on the

y

axis)? ((b)) What is the potential at the point

r = 0.40\,\text{m}

\theta = 90^\circ

\phi = 90^\circ

(outside the shell, on the

y

axis)?

Browse the problem library