Induced EMF on a primary coil by a secondary coil

[KaiserBrandon]

1. Derive an equation to find the induced EMF on an inner solenoid by a changing current on an outer solenoid.

Homework Equations

We're given the equation EoRMS=(No*Ai*(2*pi*f)*(permeability constant)*IiRMS)/Li for the induced EMF on the outer solenoid by a changing current in the inner. I need an equation to replace this for when it's the other way around.

The Attempt at a Solution

I have no idea where to even begin, I just need a hint as to how I should start.

 

[Andrew Mason]

1. Derive an equation to find the induced EMF on an inner solenoid by a changing current on an outer solenoid.

Homework Equations

We're given the equation EoRMS=(No*Ai*(2*pi*f)*(permeability constant)*IiRMS)/Li for the induced EMF on the outer solenoid by a changing current in the inner. I need an equation to replace this for when it's the other way around.

The Attempt at a Solution

I have no idea where to even begin, I just need a hint as to how I should start.

Start with Faraday's law for a coil:

$$V_{induced} = -N\frac{d\phi}{dt} = -NA\frac{dB}{dt}$$

where N is the number of coils in the inner coil, B is the magnetic field and A is the area enclosed by the coils.

Can you apply Ampere's law to determine the relationship between the rate of change of current in the outer coil and dB/dt?

AM