# Magnetic Flux through a wire loop

## Homework Statement

I understand that if we have a solenoid with AC current running through it, it will create a changing magnetic flux.

Suppose now we place the solenoid in the centre of the a single loop wire, according to faraday's law of induction, that single loop wire will have a emf, and hence a current running through it.

Question i have is, according to ampere's law, there is no magnetic field outside the solenoid. So, how does the single loop wire knows that there is a changing magnetic flux in its centre and respond to it?

Also, if i keep increasing the size of the loop (i know Area of loop doesn't matter affect emf, only the flux from the solenoid does), will the emf/ current eventually drop to zero? Logic tells me it does, of course.

Any help will be greatly appreciated.

Also, if i keep increasing the size of the loop (i know Area of loop doesn't matter affect emf, only the flux from the solenoid does), will the emf/ current eventually drop to zero? Logic tells me it does, of course.

Resistance will increase to current will tend to 0 ?

first one ... i dunno :p

the magnetic field outside a solenoid is small, but it is not zero (unless the solenoid has infinite length).

supratim1
Gold Member
it is due to induced electric field, which produces the current.

SammyS
Staff Emeritus
Homework Helper
Gold Member
Ampère's Law doesn't say the B filed is zero. It says the line integral of B·d is zero.

This is similar to using Gauss's Law for electric field and claiming that the E field is zero outside of any region which contains no net charge.

In this case, we take an ideal solenoid, infinitely long. In this case, there should be zero, not even small, magnetic field outside the solenoid. If we were to put a compass immediately outside the solenoid, it would not be deflected.

How then can the wire loop know that there is a changing magnetic flux in its centre.

SammyS
Staff Emeritus
Homework Helper
Gold Member
The solenoid mentioned in the Original Post is not infinitely long as I read the problem.

So now we make it an infinitely long solenoid, an ideal perfect solenoid. The situation will still be the same. There is no magnetic field outside the solenoid, but the wire loop some how knows that there is a flux going through it.

Why is this so?

So now we make it an infinitely long solenoid, an ideal perfect solenoid. The situation will still be the same. There is no magnetic field outside the solenoid, but the wire loop some how knows that there is a flux going through it.

Why is this so?

hi,

The B-field outside the solenoid is zero, not the E-field. E-fields drive current.

if you have long straight B-field lines that are changing in time, as in your example, then there are E-field lines that form concentric circles around the B-field lines. This E-field is what drives the current in the outer loop of wire.

cheers.

Oh, got it. Thanks eczeno. It was mentioned in the previous post, but the subtlety was lost to me.

cheers.