St. Vincent College
PH 252: Electromagnetic Fields
Exam 4
10/22/2010
1. (35 pts) In class, we started a problem involving a spherical shell of charge carrying charge density
σ(θ) = P0cos θ. We applied boundary conditions on the potential at r→ ∞ and r→0, using a partial
solution to Laplace’s Equation in spherical coordinates, and arrived at potentials
ϕin =A1+C1rcos θ(r < R)
ϕout =B2
r+D2
r2cos θ(r > R)
Apply the remaining boundary conditions, ϕin =ϕout at the shell (r=R) and E⊥out −E⊥in =σ/ǫ0, to
solve for the remaining undetermined coefficients in the two potentials. Make sure to write out and
clearly identify the final potentials, both for r < R and r > R.
