# How Do You Calculate the Magnetic Moment and Torque of a Rectangular Loop?

• superslow991
In summary: The magnetic moment of a loop of wire is proportional to the current flowing through it and in the same direction as the field. The torque exerted on the loop by the magnetic field is proportional to the magnitude of the current and the area of the loop.
superslow991

## Homework Statement

A 15-turn rectangular loop of wire of width 10 cm and length 20 cm has a current of 2.5 A flowing through it. Two sides of the loop are oriented parallel to a uniform magnetic field of strength 0.037 T, and the other two sides are perpendicular to the magnetic field. (a) What is the magnitude of the magnetic moment of the loop? (b) What torque does the magnetic field exert on the loop?

## Homework Equations

(a)- μ0 = NIA
(b)- torque = μ0 x B

## The Attempt at a Solution

have the answer but would like to know the direction of A( area), the μ0, and also the direction of the field (B) and the torque.

I believe A's direction is perpendicular to the loop?
im unsure for the mu, Torque, and field

Last edited:
superslow991 said:
I believe A's direction is perpendicular to the loop?
Yes.
The magnetic moment is in the same direction as A.
The field direction is incompletely specified here as in the plane of the loop and perpendicular to two sides (which two?)
The torque is given by ##\vec{\mu}\times \vec{B}##, but only its magnitude can be calculated because the direction of the field is unknown.

superslow991
kuruman said:
Yes.
The magnetic moment is in the same direction as A.
The field direction is incompletely specified here as in the plane of the loop and perpendicular to two sides (which two?)
The torque is given by ##\vec{\mu}\times \vec{B}##, but only its magnitude can be calculated because the direction of the field is unknown.
So is the field's direction perpendicular to the current and magnetic moment?

superslow991

## 1. What is the magnetic moment of a loop?

The magnetic moment of a loop is a measure of the strength and direction of the magnetic field produced by a current-carrying loop. It is defined as the product of the current flowing through the loop and the area enclosed by the loop.

## 2. How is the magnetic moment of a loop calculated?

The magnetic moment of a loop can be calculated using the formula: m = I * A, where m is the magnetic moment, I is the current flowing through the loop, and A is the area enclosed by the loop.

## 3. What factors affect the magnetic moment of a loop?

The magnetic moment of a loop is affected by the strength of the current flowing through the loop, the size and shape of the loop, and the material the loop is made of. Additionally, the orientation of the loop with respect to an external magnetic field can also affect its magnetic moment.

## 4. Why is the magnetic moment of a loop important in physics?

The magnetic moment of a loop is an important concept in physics because it helps us understand the behavior of magnetic fields and their interactions with other objects. It is also key in the development of technologies such as electric motors and generators.

## 5. How can the magnetic moment of a loop be used in practical applications?

The magnetic moment of a loop is used in a variety of practical applications such as in electric motors, generators, and magnetic resonance imaging (MRI) machines. It is also used in research and development in areas such as magnetic levitation and magnetic data storage.

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