# Magnetic Dipole Moment of a Coil

## Homework Statement

You have a coil of N turns, with current I through it.

It is in a magnetic field B, which causes it to feel a torque.

Give an expression for its magnetic dipole moment.

## The Attempt at a Solution

Well, I know magnetic dipole moment is A x I

So for a coil of N turns it should be A x IN.

The problem is, A isn't specified in the problem, which makes me wonder if there's a better/different way to do this. Any ideas?

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Redbelly98
Staff Emeritus
Homework Helper
There's an equation that relates torque to B and magnetic dipole moment. Are we to assume the torque is a known, eg. "the coil experiences a torque T"?

Without thinking through the problem completely, I'd say that equation is likely to be helpful here.

Yeah, that equation is t = u x B

However the next question is, "give an expression for the torque". So I think I need to find u first, then use that to find t = u x B.

Thanks though!

Are any numbers given in the problem at all?

Redbelly98
Staff Emeritus
Homework Helper
Weird. I don't see how you can answer this, without having the area ... or some information (radius of circle, side-length of a square, etc.) that could be used to calculate area.

The reason I asked if any numbers were given is that the phrasing "give an expression for" could mean that it's a symbolic reasoning problem (in which case you already have the answer for the first part - you gave it in your original post - and the second part is simply a matter of plugging your answer for the first part into the relevant equation).

Nope, no numbers are given at all.

Last edited:
Alright. Well, if there are no numbers, then you're just supposed to find a symbolic expression for the quantities. You gave an expression for mu in your first post: mu = N (A x I). Plug that into the formula for torque, and you'll have your expression for torque. You can assume that A is a given, since there's no way to get mu or the torque without A.

Okay, thank you so much!