How Does Gauss's Law Apply to a Uniformly Charged Sphere?

[yaro99]

Homework Statement

A charged paint is spread in a very thin uniform layer over the surface of a plastic sphere of diameter 10.5 cm, giving it a charge of -22.3 µC.

(a) Find the magnitude of the electric field just inside the paint layer.
(b) Find the magnitude of the electric field just outside the paint layer.
(c) Find the magnitude of the electric field 5.00 cm outside the surface of the paint layer.

Homework Equations

$$E=\frac{q}{4\pi\epsilon_0 r^2}$$

The Attempt at a Solution

I got (a) correct (E=0), but I'm getting wrong answers for (b) and (c)

For (b), the radius is 0.0525m, so:
$$E = \frac{-22.3\times 10^{-6}}{4\pi (0.1025)^2(8.854\times 10^{-12})} = -7.272\times 10^7$$

For (c), r=0.0525+0.05=0.1025, so:
$$E = \frac{-22.3\times 10^{-6}}{4\pi (0.1025)^2(8.854\times 10^{-12})} = -7.272\times 10^7$$

EDIT: for some reason my latex code isn't displaying properly, so here are pics of my equations:
EDIT 2: fixed it

 

[Simon Bridge]

Homework Statement

A charged paint is spread in a very thin uniform layer over the surface of a plastic sphere of diameter 10.5 cm, giving it a charge of -22.3 µC.

(a) Find the magnitude of the electric field just inside the paint layer.
(b) Find the magnitude of the electric field just outside the paint layer.
(c) Find the magnitude of the electric field 5.00 cm outside the surface of the paint layer.

Homework Equations

$$E=\frac{q}{4\pi\epsilon_0 r^2}$$

The Attempt at a Solution

I'm getting wrong answers for (b) and (c)

For (b), the radius is 0.0525m, so:$$E = \frac{-22.3\times 10^{-6}}{4\pi (0.0525)^2(8.854\times 10^{-12})} = -7.272\times 10^7$$

> (-22.3e-6)/(4*pi*(0.0525^2)*(8.854e-12))
ans =  -7.2717e+07

... hmmm, if this is being computer mediated, then you should check rounding and the exact form of the input, units, stuff like that. Perhaps they'll accept $\small -7.27\times 10^7$V/m

EDIT: for some reason my latex code isn't displaying properly

That's because you didn't use only latex markup inside the latex tags.
Use the "quote" button (below, right) to see what I did.