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

[SpringWater]

Homework Statement

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?

Homework Equations

All relevant equations are attached

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.

 

[rude man]

Homework Statement

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?

Homework Equations

All relevant equations are attached

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)?

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.

 

[SpringWater]

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.

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?

 

[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.

 

[SpringWater]

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.

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

 

[rude man]

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

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.