Question

A region of space has a ball of total positive charge Q whose charge is distributed spherically symmetrically with a charge density of

ρ(r)= α(1−r^2/a^2) for 0 ≤ r ≤ a

ρ(r) = 0 for r ≥ a

Here α is a positive constant whose units are coulombs per cubic meter.

a. Determine α in terms of Q and a.

b. Use Gauss’s law to determine the magnitude of the electric field as a function of r for both regions. Express your answers in terms of Q.

c. At what value of r is the magnitude of the electric field the largest?

Answer 1