Question

PHYS 272 Problem Set 2, Turn-in Part Please provide one page per problem and ensure that your name is written on the top of each page. Otherwise, both problems may not be graded Problem 1 In the figure shown below, a solid sphere of radius = 3.90 cm is concentric with a spherical conducting she of nner radius b 2.00a and outer radius c 2.40a The sphere has a net uniform charge q,-+6.70 fC: the shell has a net charge q,-9- What is the magnitude of the electric field at radial distances (a) r0 cm, (b) r a/2.00, (c) r = a, (d) r = 1.50a, (e) r = 2.30a, and (f) r = 3.50a? What is the net charge on the g)nner and (h) outer surface of the shell?

Answer 1

If we read carefully in the sentence, we can observe that the distributions of charges in both the sphere and the shell have spherical symmetry around their common center. To determine the electric field at several distances from said center, a Gaussian surface will be drawn in regions of interest.

To determine the electric field E inside the solid sphere, let's consider a Gaussian surface of radius r <a. Given that inside a conductor in electrostatic equilibrium it is not possible to have charge, we see that q = 0 and consequently based on the Gaussian law and in the symmetry E = 0 for r <a

In conclusion for option (a) and (b) E = 0

For r = a we construct a Gaussian spherical surface of radius, where the electric field is given by:

$E=\frac{q}{4\pi \epsilon _{0}r^{2}}=\frac{q}{4\pi \epsilon _{0}a^{2}}=\frac{k_{e}q}{a^{2}}$

for r> c the total load is the load of the solid spherical minus the charge of the shell, consequently the net charge is zero and the electric field is zero for r> c.

the charge on the inner surface of the spherical shell must be -q to cancel the charge + q there is on the solid sphere. Since the charge on the shell is -q we conclude that on the outer surface it must have charge q