Electric Field inside a charged ring

[yeezyseason3]

Homework Statement

Given a charged ring in 2-d, what is the e-field inside the ring?

Homework Equations

Epoint = kq/r^2

The Attempt at a Solution

This isn't a homework question, but more of a problem I keep running into whenever I think about it. I assumed it was 0. I came to this conclusion because the gradient of potential is electric field, and potential within a ring is constant, therefore electric field is 0.

 

[Simon Bridge]

You can check by considering that the electric field is a vector... the field dead center is easy, you are wondering about off-center right?

 

[yeezyseason3]

You can check by considering that the electric field is a vector... the field dead center is easy, you are wondering about off-center right?

Yea I am, I tried integrating and it got really messy, I assumed I was doing something wrong and instead assumed that potential is constant and hence e field is 0.

 

[Simon Bridge]

You "assumed" the potential was constant?
Didn't you calculate it?

Trying to do the vector calculus is nasty - try exploiting the line of symmetry through the center of the ring and the point you want to find the field for ... if you integrate equal angles either side of that line for a short arc, you should be able to find another similar arc on the opposite side that will integrate to equal and opposite field.

 

[BvU]

I tried integrating and it got really messy

If you show what you did, perhaps we can help ?