Magnetic Field with Time Dependence

[deenuh20]

Homework Statement

A magnetic field with the time dependence shown in the figure below is at right angles to a N=197 turn circular coil with a diameter of d=4.2 cm.


What is the induced EMF in the coil at t=7.5ms in mV?

See attached graph

Homework Equations

|EMF|= N*|change in magnetic flux/change in time|

The Attempt at a Solution

First Attempt:
I first found Area by pi*(.042m/2)^2 and got 0.001385m^2. Then, I found the slope of the line between 5 and 10 ms, which was -0.006 T/ms. Then, I multiplied this slope by 7.5ms to see what the magnetic field at 7.5ms was, and I got -0.45T. Then, I used this value to find the magnetic flux which was (0.001385m^2)(-0.045T) and got -6.235*10^-5. Then, I took this value, divided by 7.5ms, and got -0.00831. Then, I multiplied this by 197 and got -1.63707 V. I divided this by 1000 and got -0.001637mV, but this answer is not being accepted.

 

[Doc Al]

First Attempt:
I first found Area by pi*(.042m/2)^2 and got 0.001385m^2.

Good.

Then, I found the slope of the line between 5 and 10 ms, which was -0.006 T/ms.

All good, so far. And this is almost all you need.

Hint: You've already calculated the rate of change of the field, so what's the rate of change of the flux?

(The flux doesn't matter--only the rate of change of the flux.)

 

[deenuh20]

To find the rate of change of the flux, I did:

(B @ 10ms * Area) - (B @ 5ms * Area) all divided by (10ms-5ms)
(-0.01T*0.001385)-(0.02T*0.001385)/(5ms) and got 4.155*10^-5 as the rate of change of the flux

I then multiplied 4.155*10^-5 by 197, and got 0.008185, which I then divided by 1000, and got 8.18535mV, however, this is still not the right answer.

Is my reasoning flawed or am I missing an essential step?

 

[Doc Al]

To find the rate of change of the flux, I did:

(B @ 10ms * Area) - (B @ 5ms * Area) all divided by (10ms-5ms)
(-0.01T*0.001385)-(0.02T*0.001385)/(5ms) and got 4.155*10^-5 as the rate of change of the flux

Your reasoning is fine; check your arithmetic.

 

[deenuh20]

Ok, let's try this step by step:

To find the rate of change of the flux, I did:

(B @ 10ms * Area) - (B @ 5ms * Area) all divided by (10ms-5ms)
(-0.01T*0.001385)-(0.02T*0.001385)/(5ms) and got 4.155*10^-5 as the rate of change of the flux

I redid my arithmetic here, and as the rate of change of flux, I now got -0.00831

Is this correct?

Also, Thank you very much for your help!

 

[Doc Al]

Looks good to me. (Units: T/s)

 

[deenuh20]

I redid my arithmetic here, and as the rate of change of flux, I now got -0.00831

Ok, now that I have the rate of change of flux, in order to find the induced EMF, in mV:

I multiplied the rate of change of flux by the number of turns (197)

(-0.00831 T/s)(197)= -1.63707 V

then to get mV: -1.63707 V/1000 = -0.001637 mV

Correct?


If this is the correct way to do it, it is still the wrong answer when I enter it in my homework online

 

[deenuh20]

I multiplied the rate of change of flux by the number of turns (197)

(-0.00831 T/s)(197)= -1.63707 V

then to get mV: -1.63707 V/1000 = -0.001637 mV

I got it! I figured out what I was doing wrong. I had to divide by 10^-3, not 1000, and got 1637.07 mV, which was the right answer. Thanks for all your help!

 

[Doc Al]

then to get mV: -1.63707 V/1000 = -0.001637 mV

Check this step. (How many mV in a Volt? )

(edit: Looks like you figured that out on your own!)