Question

The plane of a rectangular loop of wire with a width of 5.00cm and a height of 8.00cm is parallel to a magnetic field of magnitude 0.150 T. The loop carries a current of 7.00 A.

What torque acts on the loop?

What is the magnetic moment of theloop?

What is the maximum torque that can be obtained with the sametotal length of wire carrying the same current in this magneticfield?

Answer 1

Concepts and reason

The main concepts used to solve the problem are Torque and magnetic moment.

Initially, use the expression of the torque to calculate the torque. Later, use the expression magnetic moment to calculate the magnetic moment of the loop.

Finally, calculate the maximum torque acting on the wire carrying current.

Fundamentals

The expression to calculate the magnetic moment is,

Here, I is the current, A is the area, and is the magnetic moment.

The expression to calculate the torque on the loop is,

Here, is the magnetic moment, B is the magnetic field, is the torque, and is the angle between magnetic moment and magnetic field.

The maximum torque acting on the loop is expressed as follows:

Here, I is the current, A is the area, B is the magnetic field, and is the maximum torque.

(A)

Calculate the torque acting on the loop.

The expression to calculate the torque on the loop is,

Here, is the magnetic moment, B is the magnetic field, is the torque, and is the angle between magnetic moment and magnetic field.

The area of the rectangular loop is calculated as follows:

Here, A is the area, w is the width, and h is the height.

Substitute for w and for h in expression .

Substitute for A , for B , 7.00 A for I , and for in expression .

(B)

The expression to calculate the magnetic moment is,

Here, I is the current, A is the area, and is the magnetic moment.

Substitute for I and for A in expression.

(C)

Calculate the maximum torque.

The maximum torque acting on the loop is expressed as follows:

Here, I is the current, A is the area, B is the magnetic field, and is the maximum torque.

Calculate the area of the circular loop by using the circumference.

The circumference of the circular loop is,

The circumference is expressed as follows:

Substitute 26.0 cm for C in expression .

The area of the circular loop is,

Substitute 0.0414 m for r in expression .

Substitute for , for B, and for in expression .

Ans: Part A

The magnitude of the torque acts on the loop is .

Part B

The magnetic moment of the loop is .

Part C

The maximum torque that can be obtained with the same total length of wire carrying the same current in this magnetic field is .