- #1
1v1Dota2RightMeow
- 76
- 7
Homework Statement
A dielectric sphere of radius R with uniform dielectric constant ε has an azimuthally symmetric density charge σ = σ0 cos θ placed on the surface. Outside the sphere is vacuum. (a) Obtain the electrostatic potential inside the sphere, φin. (b) Obtain the electrostatic potential outside the sphere, φout. (c) What is the electric field inside the sphere?
Homework Equations
##\int \vec{D} \cdot \vec{dA}=Q_{free,enc.}##
The Attempt at a Solution
I'm not sure if my approach was correct. I assume not because part c) says to find the electric field, yet I found it without needing to find the potential. I'm sure I went wrong somewhere.
**My attempt:**
I draw a Gaussian sphere around the given sphere. Then I find ##\vec{D}##, the electric displacement.
##\int \vec{D} \cdot \vec{dA}=Q_{free,enc.}##
##D=\frac{\sigma_0 \cos \theta R^2}{r^2} \quad ; \quad r>R##
Using this, I can find the electric field by ##\vec{D}=\epsilon \vec{E}##, but this doesn't feel right. Normally, with these types of problems there's a reason to solve the steps in order.