A circular wire loop of radius 15.0 cm carries a current of 2.60 A. It is placed so that the n

Name: Problem 56, Chapter 28: Fundamentals of Physics
Uploaded: 2021-07-14T15:28:57-08:00
Duration: 2 min 34 s
Channel: Sheh Lit Chang
Description: A circular wire loop of radius 15.0 cm carries a current of 2.60 A. It is placed so that the normal to its plane makes an angle of 41.0^∘ with a uniform magnetic field of magni- tude 12.0 T. (a) Calculate the magnitude of the magnetic dipole moment of the loop. (b) What is the magnitude of the torque acting on the loop?

step 1 In this question, we have a coil of wires, circular wire loop, okay? So that looks that is orien

Question

A circular wire loop of radius $15.0 \mathrm{~cm}$ carries a current of $2.60 \mathrm{~A}$. It is placed so that the normal to its plane makes an angle of $41.0^{\circ}$ with a uniform magnetic field of magni- tude $12.0$ T. (a) Calculate the magnitude of the magnetic dipole moment of the loop. (b) What is the magnitude of the torque acting on the loop?

   A circular wire loop of radius $15.0 \mathrm{~cm}$ carries a current of $2.60 \mathrm{~A}$. It is placed so that the normal to its plane makes an angle of $41.0^{\circ}$ with a uniform magnetic field of magni-
tude $12.0$ T. (a) Calculate the magnitude of the magnetic dipole moment of the loop. (b) What is the magnitude of the torque acting on the loop?

Fundamentals of Physics

David Halliday,… 10th Edition

Chapter 28, Problem 56

Instant Answer

Solved by Expert Sheh Lit Chang

07/14/2021

Step 1

For a circular loop, the area A is given by πr², where r is the radius of the loop. Show more…

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A circular wire loop of radius $15.0 \mathrm{~cm}$ carries a current of $2.60 \mathrm{~A}$. It is placed so that the normal to its plane makes an angle of $41.0^{\circ}$ with a uniform magnetic field of magni- tude $12.0$ T. (a) Calculate the magnitude of the magnetic dipole moment of the loop. (b) What is the magnitude of the torque acting on the loop?

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Key Concepts

Magnetic Dipole Moment

The magnetic dipole moment is a measure of the strength and orientation of a magnetic source, such as a current-carrying loop. For a loop, it is defined as the product of the current and the area of the loop. This concept is fundamental in electromagnetism and is used to describe how the loop interacts with external magnetic fields, particularly in determining the torque and potential energy of the system.

Torque on a Magnetic Dipole

When a magnetic dipole is placed in a uniform magnetic field, it experiences a torque that tends to align the dipole with the field. The magnitude of this torque is given by the cross product of the magnetic dipole moment and the magnetic field, typically calculated as ?B sin(?), where ? is the angle between the dipole moment and the magnetic field. This concept is essential for understanding the behavior of magnetic materials and devices under the influence of external magnetic fields.

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