Is a moving magnet the only way to induce a current?

[an_single_egg]

Homework Statement

My class was watching a video on electricity and magnetism, and after showing how current is induced in a loop of wire when a magnet moves through it, our teacher asked us if there is another way to induce current in a loop of wire - he told us that there were in fact two other ways.

2. The attempt at a solution

I understand why the magnet induces current - the current opposes the direction of the magnetic field to resist a change in flux. So in order to induce current a different way, my thinking was you had to induce flux without changing the magnetic field.

I think a change in area of the loop of wire could also cause an induced current, since Flux = B * A. So, increase or decrease the radius. But I think that only counts as one other way, I'm not sure about how to induce current another way.

 

[TSny]

Yes, changing the area is one way. Good.

Does the formula Flux = BA apply to all situations, or only to situations where the B field is perpendicular to the plane of the loop?

 

[an_single_egg]

Flux = BA but BA is technically the dot product... so yes, but when the magnetic field is NOT perpendicular you need to multiply BA by $cos\theta$, where theta is the angle between B and A.

So you could also changed induced current by tilting the loop?

 

[TSny]

Yes. Tilting (or rotating) the loop is another way to induce a current in the loop.

 

[an_single_egg]

Thank you!

 

[Vv anand]

Consider keeping magnet stationary and move the loop forwards and backwards.
How about that?

 

[cromata]

There are 3 ways, first two, as you said are:
1)moving magnet through loop, or moving loop
2)changing the surface that loop closes
3)if you have electromagnet and put it through loop you can change the strength of that magnetic field by changing current in that electromagnet and that way current will be induced in the loop