# Homework Help: Introductory Electromagnetics: induced E-field

1. May 30, 2010

### nonequilibrium

1. The problem statement, all variables and given/known data

"You have an ideal solenoid with n windings per meter, with a current I = I' sin(wt) going through it. Calculate the induced electric field inside and outside the coil. Side: compare with dipole antenna."

2. Relevant equations

Maxwell equations
B = n mu I (magnetic field inside a perfect coil)

3. The attempt at a solution
Shall I assume that we have to calculate the E-field induced by the changing B-field that is in its turn induced from I? Or is there a more primary E-field I'm forgetting...

So if I imagine a coil laying for me from left to right with the B-field inside at a certain moment pointing to the left, I can take a vertical slice. The E-field at a distance r from the center of the solenoid will be pointing perpendicular on the B-field. Due to symmetry, I can argue that in a circle with a radius r (smaller than the radius of the solenoid) the E field is the same in size all over the circle. So with Faraday's Law:

E 2pi r = d(n mu I pi r²)/dt = n mu I' pi r² w cos(wt)

So inside the solenoid: E = n mu I' r w cos(wt) / 2?

For outside the solenoid, I think I can take B = 0, and then with the same symmetry reasoning, I get E ~ 1/r outside the solenoid.

As for the dipole antenna: they're in principle the same? (causing EM-radiation at a distance) That last question is a bit vague...

A difference between the two is that the E-field with a dipole antenna is more "direct", in a way that the charges themselves generate the E-field. Here the E-field is very secondary, only coming from a changing B-field that was induced itself... Is this an important difference?