Electric Potential of Ring of Charge: Q, R, x

[tag16]

Homework Statement

What is the electric potential a distance x above the center of a ring of charge Q with a
radius R? Derive the electric field from this relationship.

Homework Equations

V=k_e\intdq/r = k_e\intdq/(\sqrt{}a^2+x^2)

The Attempt at a Solution

V= k_e/(\sqrt{}a^2+x^2)\int dq=k_eQ/(\sqrt{}a^2+x^2)

E_x=-dV/dx= -k_eQ(d/dx)(a^2+x^2)^-1/2
= -k_e(-1/2)(a^2+x^2)^-3/2(2x)
E_x= k_ex/(a^2+x^2)^3/2 Q

Is this right? If not what is?

 

[kuruman]

Your expressions are correct although, strictly speaking, the given radius of the ring is R not a.

 

[tag16]

opps...I think I was looking at another problem when I wrote that. Thanks