Electric field at perpendicular distance R due to a Solenoid

[ElijahRockers]

Homework Statement

A solenoid as viewed from the left has a current carrying wire wrapping around it counter clockwise. The current travels from left to right. The current varies as:

$$I$$=$$I_0sin(wt)$$

According to Faraday's law, this will result in electric field. From symmetry, the electric field on a concentric circle is constant, and the electric field lines are concentric. Apply Faraday's law on a concentric circle of radius r to find an expression for the electric field at a perpendicular distance r from the solenoid.

Homework Equations

I believe I am supposed to be using Faraday's Law:

Integral of E.dS = -d/dt(Magnetic flux)
(Sorry, still trying to figure out how to use latex.)

The Attempt at a Solution

Well, we just finished doing Lenz's Rule, and I was good up until he brought electric field into it. Do I have to replace E in terms of I? I guess I just really don't get it, and I can't find it anywhere in his online notes or on the web. Help!

 

[member 553083]

EDIT: I figured it out. I needed to use the equation Integral of E.dS = -1/c d/dt(Magnetic flux)where c is the speed of light. The integral was over a circular path, so it ended up being 2πrE = -1/c d/dt(Magnetic flux). From there, I replaced the magnetic flux with μ0I_{0}sin(wt) and solved for E.