Electrostatics Problems

Problem 1 (20pts)
This problem is comprised of two independent parts.
a) Determine whether the field f = (r
2 + 1/r3
)(3 cos2
θ −1) can serve as an electrostatic potential
in a charge-free region of space.
b) Find whether the field F = er sin θ/r can represent a steady-state, that is, time-independent
current density.

Problem 2 (30pts)
A sphere of radius a, located in free space, is uniformly charged with a charge Q. The sphere is
surrounded with a spherical shell of inner and outer radii b and c, respectively, such that a < b < c.
The spherical shell carries a charge −Q uniformly distributed over its volume. Determine the
electric field everywhere.



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