# Magnetic Field inside Solenoid and EMF

1. May 5, 2009

### jderm

A small loop of area A is placed inside a long solenoid that has n turns per meter and carries a sinusoidally varying current of amplitude i. The central axes of the loop and solenoid coincide. If i = i0sin ωt, find the emf in the loop.

EMFinduced = - d($$\phi$$B)/ dt
$$\phi$$B=BA
Bsolenoid= $$\mu$$0ni

The product of B and A = A$$\mu$$0ni0sin (ωt)
So the derivative of $$\phi$$B with respect to time:
=A$$\mu$$0ni0cos (ωt) ω
so;
EMFinduced = - A$$\mu$$0ni0cos (ωt) ω

Apparently this is incorrect. I'm sorry about the sloppy formatting, could someone help me out with this?

2. May 7, 2009

### Illuminitwit

EMF = nABω sinωt
F(magnetism) = B • i • l
F(mag) = qvB

I don't know if that helps much, but those are a few more equations that might apply, although I think you already had them in various forms. If you had the magnitude of electrical/magnetic force or the length it might be easier. Sorry...