Calculating Magnetic Flux Change for Rotating Wire in Magnetic Field

[tomwilliam]

Homework Statement

If a loop of wire starts off horizontal, in a magnetic field angled 12º from the normal to the surface of the loop, and then rotates 180º in a constant magnetic field of magnitude B, what is the magnitude of the change in magnetic flux?

Homework Equations

Flux = A.B cos theta

The Attempt at a Solution

The way I see it, it should start off as:
Flux = Area x B cos 12º
then rise to its peak when perpendicular to the direction of the magnetic field
Flux = Area x B cos 0º
then down to 0 when parallel,
Flux = Area x B cos 90º
then back to the starting point, hence a overall magnitude change of 0.
Is this correct?
Thanks

 

[Mindscrape]

Yeah, you've got a good handle on it. Food for thought: what happens with the overall flux (not the magnitude), how does the current change, what about the EMF?

 

[tomwilliam]

Those are the follow on questions.
My problem is with the word magnitude.
I plotted a graph and saw that over 180º the magnetic flux goes from +1.6 (using the data I have) to -1.6. Does that mean the magnitude of the change is 3.2? Or is it 0?
Thanks

 

[Mindscrape]

Magnitude is the total, absolute value. So the magnitude of the magnetic flux is |+1.6| and |-1.6|, 1.6 in both cases. The magnitude is the same, so $\Delta |\Phi|= |\Phi_2| - |\Phi_1| = 0$. The implications, however, are different.

 

[tomwilliam]

Magnitude is the total, absolute value. So the magnitude of the magnetic flux is |+1.6| and |-1.6|, 1.6 in both cases. The magnitude is the same, so $\Delta |\Phi|= |\Phi_2| - |\Phi_1| = 0$. The implications, however, are different.

I appreciate what you're saying. In this case, shouldn't the question read "what is the change in the magnitude of the magnetic flux?"?
It actually says what is the magnitude of the change in magnetic flux, and I'm a bit unsure of how this affects the answer.
Thanks in advance
Tom

 

[Mindscrape]

Ah, I see what you mean. Is there a way you could put down both answers? One saying zero is if the question means change in magnitude, and another saying 3.6 if the questions means magnitude of the change.

 

[tomwilliam]

I might just do that, thanks.

After having calculated the EMF in the ring as a result of flipping it 180º in 0.2 seconds, I'm now asked whether I would expect the ring to heat up due to this induced current.

I've no idea how to justify my answer (no) which is based on everyday experience. I can calculate the (very small) EMF, and could use V=iR with an estimate for resistance to produce a rough current i, but still don't know how to justify my simple answer.
Any advice?
Thanks in advance