- #1

goohu

- 54

- 3

- Homework Statement
- see picture

- Relevant Equations
- 1) surface charge density = P * an

2) volume charge density = -\nabla \cdot P

3) Gauss law for polarization

a) Just using the equations gives us:

surface charge density = ## \rho_{\rho s} = kR^2 ##

volume charge density = ## \rho_\rho = -4kR ##

b) I am not sure here but the Q on the shell is the same as within. If that's the case we can use gauss law to find Q which I guess is the total charge.

## -Q = \int \rho_{\rho s} \cdot ds ##

My textbook states (for conductors) any introduced charge will move to the surface and redistribute itself due to repulsion. In this case the total charge on the shell is the same as "within"?

c) The E-field can also be found form gauss law. Then I assume you plug in 2a as R? This would be the standard way of solving the problem but IDK if nonconducting material is a special case?

surface charge density = ## \rho_{\rho s} = kR^2 ##

volume charge density = ## \rho_\rho = -4kR ##

b) I am not sure here but the Q on the shell is the same as within. If that's the case we can use gauss law to find Q which I guess is the total charge.

## -Q = \int \rho_{\rho s} \cdot ds ##

My textbook states (for conductors) any introduced charge will move to the surface and redistribute itself due to repulsion. In this case the total charge on the shell is the same as "within"?

c) The E-field can also be found form gauss law. Then I assume you plug in 2a as R? This would be the standard way of solving the problem but IDK if nonconducting material is a special case?