• Support PF! Buy your school textbooks, materials and every day products Here!

Electrical field outside spherical shell

  • Thread starter glederfein
  • Start date
  • #1

Homework Statement


An insulated spherical shell with its center in the origin and radius R has a surface charge density of [tex]\sigma(\theta)=\sigma_0\sin(\theta)[/tex] when [tex]\theta[/tex] is the angle from the z axis. Calculate the electrical field outside the shell at point z=R.


Homework Equations



Gauss's Law
[tex]\int\int{\vec{E}\cdot\vec{dS}}=4\pi{Q_{in}}[/tex]


The Attempt at a Solution



I tried first calculating the overall charge of the spherical shell:
[tex]Q=R^2\int_0^{2\pi}\sigma_0\sin^2\theta{d\theta}\int_0^\pi{d\phi}=\frac{R^2\sigma_0}{2}\int_0^{2\pi}(1-\cos{2\theta})d\theta\cdot\pi=\frac{1}{2}\pi{R^2}\sigma_0\cdot{2\pi}=\pi^2R^2\sigma_0[/tex]
However, I don't see how Gauss's Law can help me find the electrical field at that specific point.

Please help!
 

Answers and Replies

  • #2
anyone?

Can someone please help??

Perhaps I should somehow calculate [tex]\int{\frac{dq}{r^2}}[/tex] ?
 

Related Threads for: Electrical field outside spherical shell

Replies
2
Views
6K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
3
Views
15K
  • Last Post
Replies
10
Views
140
Replies
7
Views
6K
  • Last Post
Replies
2
Views
285
Replies
1
Views
2K
Top