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

[Bng1290]

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

Homework Statement

A circular disk of radius R and total charge Q has the charge distributed with surface charge density \eta = 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.

Homework Equations

\eta=cr where c is constant
V=(1/4pi\epsilon)(Q/r)
V=\SigmaV_i

The Attempt at a Solution

So what I did was to sum all V_i and i was able to pull (1/4pi\epsilon) 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 \eta in some way. The problem I'm having here is that I just don't understand how to work with \eta=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!