10—Partial Differential Equations 31410.37( From the preceding problem you can have a potential, a solution of Laplace’s equation, in the form
Ar+B/r^2
)
cosθ. Show that by an appropriate choice of AandB, this has an electric field that for large
distances from the origin looks likeE 0 ˆz, and that on the spherer=Rthe total potential is zero — a grounded,
conducting sphere. What does the total electric field look like forr > R; sketch some field lines. Start by asking
what the electric field is asr→R.