Electric Field of Uniformly Charged Ring

[bowdish.9]

A uniformly charged ring of radius 10.0 cm has a total charge of 58.0μC. Find the electric field on the axis of the ring at the following distances from the center of the ring. (Choose the x-axis to point along the axis of the ring.).

I know the equation I want to use is E= (kQx)/(x^2+r^2)^(3/2)
where x is distance from the center of the ring and r is the radius.

But, I don't know where this equation comes from. I know E=kq/r^2, so I'm just not sure where the x/(x^2+r^2)^(3/2) comes from.

 

[Doc Al]

Read all about it: Electric Field: Ring of Charge

 

[Chandra Prayaga]

The formula that you wrote: E = kq/r^2, is the field of a point charge. If you have a ring of charge, you have to calculate the field due to tiny pieces of the ring, each considered a point charge, and vectorially add the fields. This process, in the limit as each tiny piece tends to zero size, is called integration. If you do the integration, you will get the more complicated formula that you wrote. This is given in detail in any calculus based textbook of introductory physics