- #1

Davidllerenav

- 424

- 14

- Homework Statement
- The electric field outside and an infinitesimal distance away from a

uniformly charged spherical shell, with radius R and surface charge

density σ, is given by Eq. (1.42) as σ/0. Derive this in the following

way.

(a) Slice the shell into rings (symmetrically located with respect to

the point in question), and then integrate the field contributions

from all the rings. You should obtain the incorrect result of

##\frac{\sigma}{2\epsilon_0}##.

(b) Why isn’t the result correct? Explain how to modify it to obtain

the correct result of ##\frac{\sigma}{2\epsilon_0}##. Hint: You could very well have performed

the above integral in an effort to obtain the electric

field an infinitesimal distance inside the shell, where we know

the field is zero. Does the above integration provide a good

description of what’s going on for points on the shell that are

very close to the point in question?

- Relevant Equations
- Coulomb's Law

Hi! I need help with this problem. I tried to do it the way you can see in the picture. I then has this:

##dE_z=dE\cdot \cos\theta## thus ##dE_z=\frac{\sigma dA}{4\pi\epsilon_0}\cos\theta=\frac{\sigma 2\pi L^2\sin\theta d\theta}{4\pi\epsilon_0 L^2}\cos\theta##.

Then I integrated and ended up with ##E=\frac{\sigma}{2\epsilon_0}\int \sin\theta\cos\theta d\theta##. The problem is that I don't know what are the limits of integrations, I first tried with ##\pi##, but I got 0. What am I doing wrong?