# Homework Help: Electric Field outside charged metal sphere

1. Mar 13, 2013

### dpb613

1. The problem statement, all variables and given/known data
A metal sphere of radius 10 cm carries a charge of +2μC uniformly distributed over its surface. What is the magnitude of the electric field due to this sphere at a point 5.0 cm outside the sphere's surface?
8.0 x 109 N/C
4.2 x 106 N/C
8.0 x 107 N/C
4.0 x 109 N/C
4.0 x 107 N/C

2. Relevant equations
Based on my understanding that a charged sphere can be treated as a point charge (a charge concentrated in one point) at its center I used the equation for electric field of a point charge:
$\vec{E}=\frac{kq}{r^2}\hat{r}$
Where k is the electrostatic constant 8.99 x 109Nm2/C2 (N=Newton, m=meter, C= Coulombs)
and r is the distance from the point charge.
Note:$\hat{r}$ is the direction and is irrelevant to this question since it is asking the magnitude.
2μ=2 x 10-6

3. The attempt at a solution
The distance from the center of the sphere is 15 cm or 0.15 m
All that said I plugged in the values as follows (sorry about the formatting Latex refused to do this one):
(8.99*10^9 * 2*10^(-6))/0.15^2
And got a result (viewable here http://wolfr.am/Znug5V)of 8.0 x 105 after rounding to two significant figures. This is not one of the choices given. Please show me my mistake. Thank You.

2. Mar 13, 2013

### rude man

I got the same answer so I suspect someone made a slipup in defining the problem.

3. Mar 14, 2013

### dpb613

Still, I would appreciate feedback if anyone understands what they expect me to answer.