Net Charge of Spherical Shell +Q at Center

[tag16]

Homework Statement

A conducting spherical shell has a total net charge of +2 micro Coulombs. A point charge of Q = -3 micro coulombs is placed at the center of the sphere. What is the total net charge on the inner surface of the sphere?

Homework Equations

coulombs law= kq1q2/r^2

The Attempt at a Solution

I really have no idea where to start on this one even though I have a feeling it's actually really easy and I'm just missing something. I tried to find a similar problem in my physics book but didn't see anything, any help would be appreciated.

 

[Doc Al]

Hint: Gauss's law.

 

[tag16]

oh, ok...I thought that was used to find the flux

 

[Doc Al]

oh, ok...I thought that was used to find the flux

If you know the flux you can use Gauss's law to find the net charge. Where would you put your gaussian surface to find the charge on the inner surface of a conducting shell?

 

[tag16]

So after I find the flux would I have to use S EdA? (the S is suppose to be an integral symbol)

 

[TwoTruths]

I'm not entirely sure, but try to think of it intuitively. If you have a hollow sphere with charge, and you put some charge inside it, what will that inside charge do to the charged particles in the hollow shell? They'll move around, right? And since it's a conductor, all charge is located on the surface. But wait - shouldn't the total charge inside a cavity in a conductor be zero? Yes! So, what charge needs to be on the inner surface such that the total charge in the cavity is zero?

 

[tag16]

wouldn't the area come into play here? and since it's a sphere it would be 4pi r^2, if not then I'm still confused and if it does then I'm still confused because there is no radius given in the problem.

 

[TwoTruths]

No, the area shouldn't matter. A conductor will distribute the charges as necessary about its surface such that the electric field inside is always 0. Notice they said TOTAL charge. This means they don't care about how it's distributed over what area with what density - they just want the total.

Like Doc Al said, you can use Gauss's Law to solve this if you place your Gaussian surface correctly (that is, so you have a uniform E along the surface so the integral becomes trivial).

 

[tag16]

so it would be q(internal)/ E_0? which would be -3 microcoulombs/ E_0?

 

[Doc Al]

so it would be q(internal)/ E_0? which would be -3 microcoulombs/ E_0?

Where are you placing your gaussian surface? What's the total flux through that surface?

 

[tag16]

wouldn't you just place the surface on the inside of the sphere?

 

[Doc Al]

wouldn't you just place the surface on the inside of the sphere?

Be more specific:

The point charge is at r = 0.
The inner surface of the conducting shell is at r = r_i.
The outer surface of the conducting shell is at r = r_o.
(r_o > r_i)

Where exactly would you put your gaussian surface? Hint: Since you're trying to find the charge on the inner surface of the shell, your gaussian surface must at least contain that inner surface. Hint 2: Take advantage of known properties of conducting materials.