# Find the max induced EMF in the loop by the changing loop

1. Apr 21, 2013

### SpringWater

1. The problem statement, all variables and given/known data
I have attached the two questions. the first has a diagram.

1. Find the MAX Induced EMF (in volts) in the loop by the changing current?

2. What is the magnitude of the EMF induced in the loop by the changing current at t=.8 (seconds) answer in Volts?

2. Relevant equations

All relevant equations are attached

3. The attempt at a solution

I believe I understand most of how to find the correct solution. However I am having trouble with deciding what is E(max) (1st question)? I am assuming I include E(max)=(μ)*(n)*(N)*(A) but i am not sure if i include I(initial)???

Any help will be greatly appreciated.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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• ###### hw 11 #5,6 work.jpg
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2. Apr 21, 2013

### rude man

If all else fails, revert to dimensional analysis!
Letting E = emf, would E = (μ)*(n)*(N)*(A) be dimensionally correct?
Would E = (μ)*(n)*(N)*(A)*(i) be correct?
How about E = (μ)*(n)*(N)*(A)*(i)* (alpha)?
Hint: one of them is, the others are not.

PS otherwise what you did was fine.

3. Apr 21, 2013

### SpringWater

Thank you for the reply, I greatly appreciate it!

so here is what i have. A Volt units can be changed into a lot of different units. so

μ=(N) / (Amp)^(2)

n=turns / (meter)

N= Turns

I(initial)=Amp

Area=(meter)^(2)

alpha is (1) / (seconds) so then..

(Newton)*(Turns)*(Turns)*(meter^(2))*(Amp)
(Amp)^(2)*(meter)*(second)

then finally (N)*(Turn(in))*(Turn(out))*(Meter) / (Amp)*(second)

i am not sure how to eliminate turns?

4. Apr 21, 2013

### rude man

N is dimensionless. But watch out: n has dimensions of 1/L.

You slipped up somewhere. i needs to be in the numerator, obviously.

Make life easier for yourself: you know from your textbook that for a solenoid B = μ0*i*n and you should know emf = -N*d(phi)/dt = -N*A*dB/dt in this case. So emf must look like
emf = A*B*T-1 = A*μ0*i*n*T-1.

In other words, no need to break everything down into fundamental units.

5. Apr 21, 2013

### SpringWater

okay, I assumed that T=time constant tau or in my case alpha. the answer was correct. thank you for the help

6. Apr 21, 2013

### rude man

Alpha is not the tme constant. 1/alpha is. Alpha has units of T^(-1) as it must since you need a di/dt term in your emf.