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## Homework Statement

An insulator is in the shape of a spherical shell. The insulator is defined by an inner radius

*a*= 4 cm and an outer radius

*b*= 6 cm and carries a total charge of

*Q*= + 9

What is

*Ey*, the y-component of the electric field at point P which is located at (x,y) = (0, -5 cm)?

## Homework Equations

Φ

_{net}= Q

_{enclosed}/ ∈

_{0}= E × ∫

_{surface}dA

## The Attempt at a Solution

I found the charge density ρ:

Total charge 9e-6 C / ( 4/3 π (0.06

^{2}- 0.04

^{2})) = ρ

Then, with my Gaussian surface a sphere with radius 5 cm, I found Q

_{enclosed}

Q

_{enclosed}= ρV = ρ * 4/3 π (0.05

^{2}- 0.04

^{2})

I know that

Φ

_{net}= Q

_{enclosed}/ ∈

_{0}= E × ∫

_{surface}dA

which I can rearrange such that

E (this is what I need to find - the electric field on the surface) = Q

_{enclosed}/ (ε

_{0}* ∫

_{surface}dA)

And since ∫

_{surface}dA = 4 π r

^{2}

I can find E:

E = 1/4πε

_{0}* Q

_{enclosed}/ r

^{2}= 1/4πε

_{0}* 4.05e-6 / 0.05

^{2}= 14563800

This isn't correct, though. Where did I go wrong? I think it is in those last few equations - do I have the wrong area?

The units do work out: k has units N*m

^{2}/C

^{2}, Q

_{enc}has units C, and r

^{2}is in m

^{2}, which works out to N/C