18 March 2007

Question: Induced EMF coil-solenoid; How do areas play a role?

If a coil is placed around a solenoid that has a fluctuating current, how do the radii of the coil and solenoid (so basically, the areas) affect the induced EMF in the coil? Thanks.

Thanks for your question.

The EMF induced in the outer coil is a result of the magnetic field produced in the solenoid.

First let's consider the magnetic field produced by the solenoid, which is given by:

B=μnl

where n is the number of turns/unit length. But wait! There's no mention of area here... in fact as long as the approximation that l>>r holds (and that you are not near the ends), the magnetic field generated by a solenoid is independent of the cross-sectional area.

So let's consider the EMF induced in the coil surrounding the solenoid. This is given by:

EMF=-ΔΦB/Δt=-AperpendicularΔB/Δt

So the cross-sectional area of the coil does enter into the induced EMF.

Hope that is helpful. For a related question check out: Question: Solenoid in a coil