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

 

[tomcue]

I would first suggest reviewing the fundamental principles of electromagnetic induction. This will help in understanding the relationship between induced EMF and changing current in a solenoid.

One approach to deriving an equation for the induced EMF on the inner solenoid by a changing current on the outer solenoid is to use Faraday's law of induction. This law states that the induced EMF in a closed loop is equal to the negative rate of change of the magnetic flux through the loop.

In this case, the inner solenoid can be considered as a closed loop, and the changing current in the outer solenoid will create a changing magnetic flux through it. The equation for the magnetic flux through a solenoid is given by Φ = μNIA, where μ is the permeability constant, N is the number of turns, I is the current, and A is the cross-sectional area of the solenoid.

Using Faraday's law and the equation for magnetic flux, we can derive the equation for the induced EMF on the inner solenoid as follows:

E = -dΦ/dt
E = -d/dt (μNIA)
E = -μNAdI/dt

This equation represents the induced EMF on the inner solenoid by a changing current on the outer solenoid. It is similar to the equation given for the outer solenoid, but with the addition of the cross-sectional area of the inner solenoid.

I hope this helps in understanding the relationship between induced EMF and changing current in a solenoid. It is important to note that this is just one approach to deriving the equation and there may be other methods as well.