Electric potential at point x on the axis of a ring of charge density "eta"

Bng1290

1. The problem statement, all variables and given/known data
A circular disk of radius R and total charge Q has the charge distributed with surface charge density [tex]\eta[/tex] = cr, where c is a constant. Find an expression for the electric potential at distance z on the axis of the disk. Your expression should include R and Q, but not c.


2. Relevant equations

[tex]\eta[/tex]=cr where c is constant
V=(1/4pi[tex]\epsilon[/tex])(Q/r)
V=[tex]\Sigma[/tex]V_i

3. The attempt at a solution
So what I did was to sum all V_i and i was able to pull (1/4pi[tex]\epsilon[/tex]) and (1/sqrt(z^2+R^2) out which leaves me with Q left in the sum which I know i need to relate to [tex]\eta[/tex] in some way. The problem I'm having here is that I just don't understand how to work with [tex]\eta[/tex]=cr in such a way as to get rid of the constant c in my answer.

I feel like I'm not grasping this problem as a whole so any help would be wonderful. Thanks!

quenderin

To eliminate c, since \eta = cr, you can integrate the charge density over the disk to compute the total charge, Q. This should give you c in terms of Q and R.

Bng1290

Nice! Thanks so much!