Find the electric field a distance z from the centre of spherical

[skanda9051]

Homework Statement

Find the electric field a distance z from the centre of spherical sphere of radius R which carries uniform density B. treat Z<R (inside) and Z>R (outside)………. By using law of cosine how to solve this problem?

Homework Equations

1/4∏εo∫ (σ da/ r^2) cos(theta)

The Attempt at a Solution

substituting r by law of cosin.. r=√R^2+z^2-2Rzcos(theta)
1/4∏εo ∫[σ da/ R^2+z^2-2Rzcos(theta)]cos(theta)
i am stuck here what should i do next

 

[danielakkerma]

Hi...
Is the charge density given by a surface density, or a volume density? When talking about a sphere and not a spherical shell, one ought to remember that the inside is filled(in this case with charge).
In any case,
Try the following:
<br /> dA = rdr\sin(\theta)d\theta d\phi <br />
<br /> dV = r^2dr\sin(\theta)d\theta d\phi<br />
Phi goes from 0 to 2pi,
Theta goes from 0 to Pi.
r from zero to R.
Try it,
Daniel