# Non uniform surface charge density

1. Jul 31, 2014

hello.
The problem is : A metallic horizontal disk of radius R has been charged on its top surface with a total charge Q such that its surface charge density is "non uniform" and governed by the expression σ=q|cosθ|*r where r and θ are the polar coordinates measured from the center O of the disk.
Determine in terms of Q and R the value of q.
I tried to solve it using double integral but it didn't work.
σ=dq/ds then dq=q|cosθ|*r*rdrdθ then ∫dq/q=0R 02∏|cosθ|dθr2dr.
If any body can help thanks.

2. Jul 31, 2014

### Staff: Mentor

I'm very rusty on this, but consider this ....

In σ=q|cosθ|*r I think that q is fixed, so instead call it a constant, say, C.
Leading to dq=C|cosθ|*r*rdrdθ then ∫dq=C 0R 02∏|cosθ|dθr2dr.

You are solving for that constant C. If your textbook supplies the correct answer, does this get you closer?

3. Jul 31, 2014