24 March 2006

Question: Solenoid in a coil

If a solenoid is placed inside a coil, how does the current flowing through it affect said coil? How would you find the inductance value for the coil?



That's a very good question. Qualitatively, the solenoid (with some current running through it) establishes a magnetic field parallel to the axis of the solenoid. If a coil is then placed on the outside of it, the coil will "sense" the magnetic field established by the solenoid. If the current in the solenoid is time-varying (changing in time) then the magnetic field established by it will also change with time. The coil will then "sense" this changing magnetic field and respond to oppose the change (Lenz's law).



Quantitatively, we will have to look at what the magnitude of the magnetic field produced by the solenoid is, and how that may depend on time. The magnetic field of a solenoid is given by:

Bsol0I[N/l]

Thus, if the current, I is a function of time, the magnetic field will have the same time dependence. If, say, the time dependence is linear (eg. we ramp up the current to the solenoid at a constant rate), then we can use the slope as ΔB/Δt, which is related to the EMF:

EMF=-ΔΦB/Δt=-AperpendicularΔB/Δt

Chapter 21, Question #80 is an example of this, and might be good to look at.

I hope this is helpful and answers your question.