# EMF of an AC carrying electromagnet.

• Nev3rforev3r
In summary, the conversation discusses the concept of induced current in an AC electromagnet and the relationship between the magnetic field and the AC current. They also mention the use of electromagnets in speakers and the importance of EMF in determining amplitude. The conversation also touches on relevant formulas and equations, such as B=I*μ0/(2πr) and emf=-N*dΦ/dt, and the incorporation of ferromagnetic cores into the situation. The conversation concludes with a discussion on the correct formula for the magnetic field of a solenoid.

## Homework Statement

This problem arises from a much larger essay/lab/project thing. I know that there is an induced current in the wire of an AC electromagnet because the magnetic field is constantly changing along with the AC current, so it makes sense to me that will produce a constantly changing emf as well which could be effectively adding or subtracting voltage of the wire in the electromagnet, which in turn slightly changes the magnetic field of the electromagnet. The larger project concerns speakers, which use an electromagnet in conjunction with a permanent magnet to oscillate the driver/cone at the same frequency as the AC current with an amplitude determined by the changing voltage of the AC current. The amplitude thing makes the EMF important. That and the lower limit of the essay word count.

## Homework Equations

I didn't go quite this far into electromagnetism in my physics class, so figuring out what the relevant equations are is part of the process.

I=I0cos(2*pi*ft)
I=V/R
B=I*mu0/(2pi*r)
Not sure about the one directly above. Apparently it is just for a straight wire. If so I'd need something that relates the current in the wire to the magnetic field in the wire. I also have no idea how to incorporate the ferromagnetic core into the whole situation.
emf=-N*dPhi/dt

## The Attempt at a Solution

I=V0*cos(2*pi*f*t)/R
B=V0cos(2*pi*f*t)/(2*pi*r*R)
Phi=AV0cos(2*pi*f*t)/(2*pi*r*R)
emf=-NAV0cos(2*pi*f*t)/(2*pi*r*R*dt)
emf=NAV0f*sin(2*pi*f*t)/(r*R)

Didn't work. Also, this is the first time I've used legitimate mathematical calculus in a legitimate physics situation.

I still want to do something on my own, but it would be great if someone could fill the missing base pieces of "What formula should I use that relates I of a solenoid to the created B in a solenoid?" and "How do I incorporate the magnetic field of the core?"

Oh and let me know if I'm completely off in my concepts too, haha.

Nev3rforev3r said:
"What formula should I use that relates I of a solenoid to the created B in a solenoid?"

Nev3rforev3r said:

## Homework Equations

B=I*μ0/(2πr)

This would be formula for the magnetic flux density due to a solenoid.

Nev3rforev3r said:
"How do I incorporate the magnetic field of the core?"

Associated with the core is a physical quantity called its magnetic permeability. μ0 is called the permeability of a vacuum and is equal to 4π(10-7) H/m.

So different cores have different values for μ, the higher the value of μ, the higher the value of B and hence the emf increases.

As for your derivation you have

E=-N*dΦ/dt = -N*d/dt(BA)

A does not change with time so E=-NA*dB/dt and dB/dt = dI/dt*μ0/(2πr).

Ok so you're saying that
emf=-NA*dI/dt*μ0/(2πr).
The current in my situation is a regular AC current, so it changes according to
I=I0cos(2πft)
should apply.
dI0cos(2πft)/dt = -I02πf*sin(2πft)
if my math/brain is correct, that essentially gets me back to the answer I had before.

So was my end derivation correct? I said it was wrong because I graphed the equation of a current and then the derived emf formula and it seemed completely off. Maybe I did something wrong there? I don't remember exactly what numbers I used, but they seemed reasonable.

EDIT: Ahhh shoot I just realized that I've been leaving out the permeability of free space constant when deriving this stuff. Whoops.

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Well instead of I0, I used V0/R, just out of preference and the situation.

Also, I just found multiple sites that say, for a solenoid:
B=μ0NI/l

Is that somehow equivalent to the other formula for the magnetic field of a solenoid or was there a mistake?

Nev3rforev3r said:
Well instead of I0, I used V0/R, just out of preference and the situation.

Also, I just found multiple sites that say, for a solenoid:
B=μ0NI/l

Is that somehow equivalent to the other formula for the magnetic field of a solenoid or was there a mistake?

Yeah that if I remember correctly is for a solenoid. Sorry about that .

Haha it's fine. If you think about it, the two definitions of B are weirdly equivalent. Setting them equal to each other gives you N/l=1/2πr. 2πr is the circumference of the circular loops, N is the number of loops and l is also the height of the cylinder.

Thank you for your help, though =].