Question

A problem regarding magnetic fields and torque, prompt posted below momentarily. Still not sure if I need help, just putting it up here in case I need to ask.

Answer 1

"A single-turn wire loop 10 cm in diameter carries a 12-A current. It experiences a torque when the normal to the loop plane makes a 25 degree angle with a uniform magnetic field. Find the magnetic field strength."

Answer 2

@Pompeii00 , I'm just trying to visualize this, does a single-turn wire loop just mean it's just....a wire loop? I have no idea what "single turn" could mean otherwise.

Answer 3

That'd be my interpretation.

Answer 4

Alright, heh, unnecessarily confusing wording.

I'm aware that charged particles are affected by a magnetic field in that the field produces a force on them perpendicular to their velocity and the field, but here we don't have anything moving and we have a torque. Trying to think of the relevant equations or concepts.

Answer 5

Is there nothing moving?

Answer 6

Charged particles are moving through the wire, but nothing macroscopic.

Answer 7

yeah, but you have a current. Charges are moving. Moving charges have forces acting on them due to magnetic fields.

Answer 8

Yeah, like said, charged particles moving, just not aware what to do with that in terms of a fomula, heh...

I think I just found the relevant equation in my book, \[F = Il \times B\]

Answer 9

"Magnetic force on a current".

Answer 10

Yeah, it's the same equation you just used in the last problem.

Answer 11

Oh, yeah, because of the substitutions, neat.

Answer 12

Alright, gonna take a shot with the formula.

Answer 13

Although, hang on, I may be wrong here.

Answer 14

(Wondering about how to describe l as a vector right now.)

Answer 15

Torque. Torque is Nm for units... I think torque needs another meters, so I think you can use the equation above, but to make it torque instead of force, multiply by a length. So your length becomes the area of the loop.

Answer 16

Alright, one sec. Well, for future reference, how do we know *what* length to multiply by? It's convenient like you said to multiply through like that to get the appropriate units for Torque, but how do we know what length to choose? Is it the object arbitrarily or did you come up with a reasoning behind that?

Answer 17

Nevermind, this has to do with something called dipole moment, have no clue what that is, though, looking it up in my book now.

Answer 18

The way I remember it is that the shape of the wire is completely meaningless. Which is why it struck me as odd that you had length.

then I remembered torque is Nm.. so I realized that the area of the loop is what matters. In fact for torque, you actually multiply that whole equation by N, the number of loops. But here it isn't important because N=1.

Answer 19

\[\mu = NIA, \ \text{where A is a vector.}\]

Answer 20

Alright, cool.

Answer 21

*Oh*, so that's why there was the explicit mention of "single-turn loop" earlier in the prompt.

Answer 22

yeah it's multiplicative how many loops you have