Does it work this way (intro electrodynamics)?

[monkeykoder]

Homework Statement

Have a permanently (uniformly not radially) polarized sphere surrounded by a charged conductor
How is the charge on the conductor distributed (the added charge)?

Homework Equations

The Attempt at a Solution

Since the conductor cancels the field generated by the polarized sphere I'm thinking the added charge should distribute uniformly over the surface of the conductor is there any reason it shouldn't?

 

[gabbagabbahey]

Is the electric field produced by the polarized sphere going to be uniform over the spherical surface of the conductor? If not, why would you think that the charge distribution would be?

 

[monkeykoder]

My reasoning (probably flawed) is that the field due to the polarized sphere is taken care of through polarization of the conductor then the added charge should be free of the field.

 

[gabbagabbahey]

Definitely flawed. The polarized sphere produces some non-radial electric field. That electric field will push the free charges in the conductor around until they reach an arrangement that cancels the field. You should know that a uniform distribution of charge on a spherical surface produces an electric field that is radial...how can a radial electric field cancel a non-radial one?

Instead of guessing at the answer, try applying some of the methods and equations you've covered in your course.

 

[monkeykoder]

I've calculated the charge distribution due to the polarized sphere I can't figure out how to work in the charge that has been placed on the conducting shell.

So assuming no charge on the conducting sphere $$\sigma = \frac{3Q_{b}cos(\theta)}_{\pi b^{3}}$$

I can't find a way to include the added charge other than assuming that it distributes free of the field.

 

[gabbagabbahey]

What are $b$ and $Q_b$ supposed to represent? What is the entire original problem?

 

[monkeykoder]

b is the radius of the outer sphere $$Q_b$$ is the bound charge on the inner polarized sphere.

 

[gabbagabbahey]

Again, what is the entire original problem statement?

 

[monkeykoder]

Polarized sphere radius a conducting shell radius b. How will the added charge Q distribute over the shell. Just looking for a conceptual jump to solve.

Specifically a non-neutral conductor charged to a value Q is submitted to an electric field how do I calculate how the additional charge is distributed.

 

[gabbagabbahey]

That really does not sound like a complete problem statement to me. There is a reason why the homework template tells you to include "all variables and given/known data". Are you given the polarization? Are you told the net charge on the conductor? Are the spheres concentric?

 

[monkeykoder]

Problem I'm having is I'm trying to ask a question that helps me with a test problem I have without getting help on the test problem itself.

 

[gabbagabbahey]

Problem I'm having is I'm trying to ask a question that helps me with a test problem I have without getting help on the test problem itself.

Well, the general method is to solve Laplace's equation (Poisson's equation in regions where the charge density is non-zero) subject to the boundary conditions of your problem. And then find the surface charge density from the potential.

That being said, the idea of a take home exam (which I gather this is for) is to test your knowledge of the material and your mastery of the problem solving methods you have learned. You really should not be seeking help for an exam when you are not permitted to do so.

 

[monkeykoder]

That's why I'm having trouble asking a question in such a way as to not have the test question answered for me but to get a better grasp on the conceptual idea. I have the idea figured out now I'm pretty sure so I'll get on with it now. I'm sorry for posting this in the homework help section but I couldn't figure out how to get the conceptual part without a problem to work through.