# Charged spheres and shells

1. Aug 8, 2010

### roam

1. The problem statement, all variables and given/known data
A conducting sphere of radius, R = 5.5 cm with an excess charge of Q = -35.5 nC is surrounded by a concentric, conducting, spherical shell of inner radius, Rin = 9.5 cm and outer radius, Rout = 11.5 cm that carries an excess charge of q = -13.0 nC.

[PLAIN]http://img571.imageshack.us/img571/7821/imagex.gif [Broken]

Determine the electric field at the following radii for the aforementioned arrangement:

(a) r = 42.5 cm.

(b) r = 8.5 cm.

3. The attempt at a solution

(a) In the indicated region r>Rout. Therefore I model the charge distribution as a sphere with charge -Q and the expression for the field in this region would be

$$E=-k_e \frac{Q}{r^2}$$

$$-(9 \times 10^9) \frac{35.5}{42.5^2}=176885813.1$$

even if I convert r to meters I still get the wrong answer (correct answer: 2420)

(b) Again, I can apply Gauss's law to find the electric field. Since R<r<Rin I think I should use:

$$k_e \frac{Q}{r^2}=(9 \times 10^9) \frac{35.5}{8.5^2} = 4422145329$$

The correct answer is 44200 N/C, did I forget to convert something?
Thanks.

Last edited by a moderator: May 4, 2017
2. Aug 8, 2010

### kuruman

What is the charge enclosed by a Gaussian surface at 42.5 cm? Don't forget that both the sphere and the shell have charge on them. Also, how many coulombs to a nano-coulomb are there?

3. Aug 10, 2010

### roam

Yes, I got all the unit conversions correct but I'm still getting the wrong answer:

$$-(9 \times 10^{9})\frac{35.5 \times 10^{-9}}{(0.425)^2}=-1768.8$$

Why is that?

Last edited: Aug 10, 2010
4. Aug 10, 2010

### kuruman

It is because the charge enclosed by a spherical Gaussian surface at 42.5 cm is not -35.5 nC. What is it?