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(Solved): Consider a spherically symmetric charge distribution with a total charge Q and charge density \rho = ...
Consider a spherically symmetric charge distribution with a total charge Q and charge
density
\rho =\rho _(0)(r)/(R)
inside a radius R and which is centred inside a hollow shell with radius 2R and with
total charge -Q.
(a) Determine an expression for Q in terms of \rho _(0).
(b) Using the integral form of Gauss' law, show that the electric field (including the
direction) satisfies
vec(E)=aQr^(2)hat(r)
inside the inner sphere,
vec(E)=bQr^(-2)hat(r),
in between the two spheres and explain why the electric field is zero for r>2R.
You should determine the values of the constants a and bR Q whilst every-
thing else stayed the same? Give a physical reason to justify your answer (but
no calculation is expected).
(d) Setting the potential V to be zero at infinity, determine the value of V at the
centre of the inner sphere. You may give your answer in terms of a and b if you
could not determine their values.