Calculating Induced EMF using Faraday's Law: A Magnetic Flux Problem Solved

[YoshiMoshi]

Homework Statement

A magnetic flux of 400 micro-webers passing through a coil of 1200 turns is reversed in 0.1 sec. Calculate the average value of the e.m.f. induced in the coil. (Hint use Faraday's Law)

Homework Equations

The Attempt at a Solution

So I know that

phi = F/R Wb

phi is flux
F is magnetomotive force MMF
R is reluctance

I also know that

F = N I

F is the MMF
N is the number of turns in the coil
I is the current in each turn

I now that faradays law is

E = - N * d[phi_B]/dt

Where E is the electromotive force (EMF)
N is the number of turns in each coil
phi_B is the magnetic flux through a single loop

Given:
phi_B = 400 micro Wb
N = 1200 turns
t = 0.1 s
solve for E

I don't see how to solve this problem. I know phi_B but not the derivative of it as a function of time. I also don't know the current. Any help would be greatly appreciated.

 

[Herman Trivilino]

Assuming the magnetic flux changes at a constant rate, and it has a value of 400 microwebers right now, what will its value be 0.05 seconds from now?

 

[YoshiMoshi]

Thanks for your response. I'm not sure
phi = kt
phi(t=0) = 400 microwebers = 0
this can't be right so it has to be of the form
phi = kt + phi_o
phi = kt + 400 uW

phi(t=0.1s) = k(0.1) + 400 uW

I believe this is what it would be in 0.1 s but I'm not sure how that would work into the problem.

d[phi(t=0.1s)]/dt = k
So E = - N*k
I know N but I don't know E or k. What could I do once I know phi(t=0.1s) without knowing the constant rate of change for phi?

Thanks for your help!

 

[Herman Trivilino]

You're thinking about the math. Think first about the coil and the field lines. What do they look like when the flux is 400 microwebers? What do they look like 0.1 s later when the field has reversed its direction?

 

[YoshiMoshi]

I believe the filed lines come out of the positive side of the coil and enter the negative side of the coil. When the magnetic filed is reversed the current flows in the opposite direction, and the magnetic flux goes from counter clockwise to clockwise? This is by the right hand rule I believe. But I'm not sure how this helps? The filed lines are the same but have a different orientation. I'm not sure how this helps? Thanks for your help.

 

[Herman Trivilino]

I believe the filed lines come out of the positive side of the coil and enter the negative side of the coil.

That's a valid way to describe the way the field lines look at time t = 0.

When the magnetic filed is reversed the current flows in the opposite direction, and the magnetic flux goes from counter clockwise to clockwise?

That's not a description of the field lines. Picture them in your mind and tell us what they look like at time t = 0.1 s.

Once you answer that I shall ask you what they look like at time t = 0.05 s.