# Torque, Force, magnetic moment ()

• EvaBugs
In summary, the force on each side of a current carrying wire in a magnetic field is F=IL x B. The magnetic moment of the coil is M=ILB sin 30. The torque on the coil is T=N(IAB sin 90).

#### EvaBugs

I'm not sure I know how to start this problem.

"A rectangular coil has 16 turns and sides of length a=20 cm and c=50 cm. The coil is pivoted around the y-axis and its plane is at 30 degrees to a magnetic field B=50 k T. The current is 10 A
a)Find the force on each side
b)what is the magnetic moment of the coil?
c)What is the torque on the coil? "

How do I start this problem? I really have no idea

EvaBugs said:
I'm not sure I know how to start this problem.

"A rectangular coil has 16 turns and sides of length a=20 cm and c=50 cm. The coil is pivoted around the y-axis and its plane is at 30 degrees to a magnetic field B=50 k T. The current is 10 A
a)Find the force on each side
b)what is the magnetic moment of the coil?
c)What is the torque on the coil? "

How do I start this problem? I really have no idea

You start by learning how to find the force on a current carying wire in a magnetic field. Find that and post it and we can take it from there.

I know that F=IL x B = ILB sin 30 where I=10 L=20 and B = 50

Am I on the right track?

EvaBugs said:
I know that F=IL x B = ILB sin 30 where I=10 L=20 and B = 50

Am I on the right track?

Yes. That is a good start. Now think about how many turns of wire are carrying that current, and the fact that there are four different straight-line segments of the loop.

So, I'd have to find the force on each side individually.
For the first side:
F1 = 10A (0.2 m) i X 50 k ?

Am I supposed to find the values of B (in the i and j direction)?

So, to find the torque, I do:

Torque = N(IAB sin 90)

Once I have that, I can find the magnetic dipole moment using:
Torque= u x B ?

EvaBugs said:
So, I'd have to find the force on each side individually.
For the first side:
F1 = 10A (0.2 m) i X 50 k ?

Am I supposed to find the values of B (in the i and j direction)?

I assume you have a diagram to go with this problem, so you know which side of the coil is which, and I assume from your reply here that the two 20cm sides make the angle of 30 degrees with B. The 50cm sides make a different angle with B. You are on the right track with the first force, but there are 4 of them, and don't forget about the 16 turns. What does that do?

EvaBugs said:
So, to find the torque, I do:

Torque = N(IAB sin 90)

Once I have that, I can find the magnetic dipole moment using:
Torque= u x B ?

There is a reason why part b) was asked before part a) The magnetic moment (magnetic dipole moment) of the loop is a property of the geometry of the loop and the current it carries. The torque depends on that magnetic moment, so the moment is in fact included in the equation for the torque. You would have to know how torque depends on the moment to do things in the order of c) then b), which of course can be done if you understand where the torque equation comes from. I suggest you do b) then c) and find out how to calculate the moment directly from the porperties of the coil.

Thank for your help. I think I have figured it out

## What is torque?

Torque is a measure of the twisting force that is applied to an object. It is calculated by multiplying the force applied to an object by the distance from the pivot point to the point where the force is applied.

## What is force?

Force is a physical quantity that describes the interaction between two objects. It can cause an object to accelerate or change its motion. Force is measured in Newtons (N).

## What is magnetic moment (μ)?

Magnetic moment is a measure of the strength and direction of a magnetic field produced by a magnet or a current-carrying loop of wire. It is represented by the symbol μ and is measured in ampere-meters squared (A·m²).

## How are torque and force related?

Torque and force are related through the concept of leverage. Torque is the product of force and the distance from the pivot point, while force is the cause of torque. In other words, torque is a result of force acting at a distance.

## What factors affect magnetic moment?

The magnitude of magnetic moment is affected by the strength of the magnetic field, the orientation of the magnet or current-carrying loop, and the distance between the magnet or loop and the point where the magnetic field is measured. Additionally, the material and shape of the magnet or loop can also affect its magnetic moment.

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