E-field inside a non-conducting hollow pear.

[Aesteus]

Homework Statement

Find the electric field inside a hollow non-conducting pear with a surface charge-distribution (axially symmetric too) of σ(r,θ). The charge density σ is zero at the top of the pear, and 600 C/m^2 at the bottom.

Homework Equations

I'm not sure how to approach the problem ... maybe some application of Laplace's equation.

The Attempt at a Solution

The electric field at any point inside the pear will be the superposition of x,y, and z fields. I assume that we can use symmetry about the z-axis to our advantage.

 

[Aesteus]

Nevermind, it's just a simple application of gauss' law on the inside of the object yielding E=0 because there is no enclosed charge. (And E-z is non-zero I believe.)