# Torque on a current loop caused by a magnetic field

• greg_rack
In summary, according to the question, the torque on the coil is maximized when the magnetic field is parallel to the plane of the coil and directed upwards. However, this orientation of the field may not even be possible because the coil may not be free to rotate.

#### greg_rack

Gold Member
Homework Statement
DISCLAIMER: the statement is translated by me from Italian, and it contains a few terms which I found tricky to translate into English; forgive me in advance for any inaccuracy :)

A squared coil(##l=0.11m##) has 40 windings and traveled by a current ##I=20mA##.
##\rightarrow##Calculate the torque applied on the coil by a magnetic field ##|\vec{B}|=2.5e-2 T## lying on the plane of the coil.
Relevant Equations
$$\vec{\tau}=NI\vec{A}\times\vec{B}$$
Okay, so, the magnetic field lying(parallel) to the plane of the coil is confusing me quite a bit.
Usually, in this kind of problem, we have a magnetic field directed perpendicularly to the plane.
Considering this orientation of the field, wouldn't the torque on this sort of "elementary brush motor" be equal to ##0##(since the cross product of two parallel vectors is so)?
I think the problem is really badly formulated since it doesn't specify the center nor axis of rotation of the objects... it just speaks of "torque" without really putting it into context.

greg_rack said:
Relevant Equations:: $$\vec{\tau}=NI\vec{A}\times\vec{B}$$
Okay, so, the magnetic field lying(parallel) to the plane of the coil is confusing me quite a bit.
Usually, in this kind of problem, we have a magnetic field directed perpendicularly to the plane.
The direction of ##\vec A## is the direction of the area’s normal. You get maximum torque when the angle between ##\vec B## and the area's normal is θ=90º (when the angle between the plane of the coil and the field is zero).

It helps understanding if you work out the direction of the force on each of the four sides using (for example) Fleming’s left hand rule. Then draw diagrams showing the force on each side for θ=90º and for θ=0. (You may then also see why a DC motor needs a commutator!)

Your English is pretty good but (if it helps) I would have written:
“A square coil ... has 40 turns and carries a current ...
Calculate the torque on the coil due to a magnetic field parallel to the plane of the coil.”

greg_rack
Steve4Physics said:
The direction of ##\vec A## is the direction of the area’s normal. You get maximum torque when the angle between ##\vec B## and the area's normal is θ=90º (when the angle between the plane of the coil and the field is zero).
Honestly, my confusion laid on the fact that I intuitively considered the magnetic field parallel to the plane of the coil and directed upwards... so it would of course have caused a zero torque.
Considering instead the field directed perpendicularly to the vertical sides of the coil, of course, torque is maximized and the result is correct. By the way, I still think they should've provided a bit more detailed description of the situation under consideration(e.g. by giving the axis of rotation of the coil and the direction of the field relative to that axis), what do you think?

Steve4Physics said:
Your English is pretty good but (if it helps) I would have written:
“A square coil ... has 40 turns and carries a current ...
Calculate the torque on the coil due to a magnetic field parallel to the plane of the coil.”
Thanks a lot for the correction :)

greg_rack said:
I think the problem is really badly formulated
Anything lost in translation ?
Can we see the versione originale ?

greg_rack said:
... By the way, I still think they should've provided a bit more detailed description of the situation under consideration(e.g. by giving the axis of rotation of the coil and the direction of the field relative to that axis), what do you think?
I think the question is OK. The question only asks for the torque, it doesn't mention rotation. The coil may not even be free to rotate (in this case it would still experience a torque, but balanced by an opposite torque from whatever is holding it)!

The formula ##\vec{\tau}=NI\vec{A}\times\vec{B}## only needs the directions of ##\vec{A}## and ##\vec{B}##. No information requiring axis of possible rotation (or shape of the area) is needed.

As an additional note, are you familiar with couples? A (simple) couple is "Two parallel forces with the same magnitude but opposite in direction separated by a perpendicular distance d". The torque on the coil is a couple.

greg_rack
Steve4Physics said:
I think the question is OK. The question only asks for the torque, it doesn't mention rotation. The coil may not even be free to rotate (in this case it would still experience a torque, but balanced by an opposite torque from whatever is holding it)!

The formula ##\vec{\tau}=NI\vec{A}\times\vec{B}## only needs the directions of ##\vec{A}## and ##\vec{B}##. No information requiring axis of possible rotation (or shape of the area) is needed.

As an additional note, are you familiar with couples? A (simple) couple is "Two parallel forces with the same magnitude but opposite in direction separated by a perpendicular distance d". The torque on the coil is a couple.
Very exhaustive answer, I got the point, thank you very much!