Understanding Induced Current in a Changing Magnetic Field

[strawman]

Hi everyone. I'm a new poster here, so hopefully this is in the right sub forum:

I'm just interested in seeing if I've got the right idea with my differentiation of magnetic flux in order to find the induced current in a ring of wire, which has it's normal at, say 30° to a magnetic field (which is uniform but has magnitude changing with time). Let's say the area of the wire is A = π r^2 and the magnetic field strength changes with time according to B = c t^2, where c is a constant and t = time.

Magnetic flux:

Φ=AB cos 30°

Φ= (π r^2) (c t^2) cos 30°

Is it right to say I don't need to differentiate the cos 30, as that is just a constant? Infact, everything is a constant except t^2, therefore the rate of change of the flux is:

dΦ/dt = (π r^2) (c 2t) cos 30°

From here, I'm using Ohm's law, and dividing the above by the resistance of the wire, and I've got my induced current. Does that look right? Thanks!

 

[vanhees71]

That looks right, but should better be posted in the homework forum, because it looks like a typical homework problem about Faraday's Law of Induction.

 

[strawman]

Thanks for the reply. I thought about posting in the homework forum, though it isn't actually a homework question, I just made up the values to see if I had the idea right. But it does follow the same pattern as many questions. Not sure how to delete or move the thread?

 

[vanhees71]

No problem. Just keep in mind to post such questions in the homework forum, using the template there, and welcome to Physics Forums!