Electric Field outside charged metal sphere

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SUMMARY

The discussion centers on calculating the electric field outside a charged metal sphere with a radius of 10 cm and a charge of +2μC. The correct formula for the electric field, treated as a point charge, is given by the equation E = kq/r², where k is 8.99 x 10⁹ Nm²/C². The calculated electric field at a distance of 15 cm from the center of the sphere yields a result of 8.0 x 10⁵ N/C, which does not match any of the provided answer choices, indicating a potential error in the problem statement or answer options.

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Homework Statement


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

Homework 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

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.
 
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I got the same answer so I suspect someone made a slipup in defining the problem.
 
rude man said:
I got the same answer so I suspect someone made a slipup in defining the problem.

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

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