Find the magnetic dipole moment of the current loop given in the figure. A) Ia² (-î -ĵ+ k) B) Ia² (-k) C) Ia²(-i-)-k) D) Ia²(-k) E) Ia² (-1)

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
icon
Related questions
Question
**Finding the Magnetic Dipole Moment \( \vec{\mu} \) of the Current Loop**

Consider the problem statement:

Find the magnetic dipole moment \( \vec{\mu} \) of the current loop given in the figure.

**Options:**
A) \( I a^2 (-\hat{i} - \hat{j} + \hat{k}) \)  
B) \( I a^2 \left( \frac{1}{\sqrt{2}} \hat{j} - \frac{1}{\sqrt{2}} \hat{k} \right) \)  
C) \( I a^2 \left( -\hat{i} - \frac{1}{\sqrt{2}} \hat{j} - \frac{1}{\sqrt{2}} \hat{k} \right) \)  
D) \( I a^2 (-\hat{k}) \)  
E) \( I a^2 (-\hat{j}) \)  

**Explanation of the Diagram:**

The diagram shows a 3D representation of a rectangular loop oriented in the x-y-z coordinate system with a current \( I \) flowing through it. 

- The loop is aligned with the coordinate planes such that:
  - One surface is parallel to the xz-plane.
  - Another surface is parallel to the yz-plane. 
  - The loop creates a rectangular circuit and the dimensions of the rectangle are given as 'a' for both length and width.

Arrows indicate the direction of the current steadily flowing through the loop:

- \(\hat{x}\): The positive x-direction arrow indicates the current flowing parallel to the x-axis.
- \(\hat{y}\): The positive y-direction arrow indicates the current is flowing parallel to the y-axis.
- \(\hat{z}\): The current is flowing parallel to the z-axis.

Use the right-hand rule: Point the thumb of your right hand in the direction of the current. The curl of your fingers indicates the direction of the magnetic dipole moment (\( \vec{\mu} \)).

The formula for the magnetic dipole moment \( \vec{\mu} \) of a current loop is:
\[ \vec{\mu} = I \cdot (\text{Area Vector}) \]

Calculating the Area Vector:

If we look closely, the loop is perpendicular to the plane forming a rectangle. The effective area vectors are the summ
Transcribed Image Text:**Finding the Magnetic Dipole Moment \( \vec{\mu} \) of the Current Loop** Consider the problem statement: Find the magnetic dipole moment \( \vec{\mu} \) of the current loop given in the figure. **Options:** A) \( I a^2 (-\hat{i} - \hat{j} + \hat{k}) \) B) \( I a^2 \left( \frac{1}{\sqrt{2}} \hat{j} - \frac{1}{\sqrt{2}} \hat{k} \right) \) C) \( I a^2 \left( -\hat{i} - \frac{1}{\sqrt{2}} \hat{j} - \frac{1}{\sqrt{2}} \hat{k} \right) \) D) \( I a^2 (-\hat{k}) \) E) \( I a^2 (-\hat{j}) \) **Explanation of the Diagram:** The diagram shows a 3D representation of a rectangular loop oriented in the x-y-z coordinate system with a current \( I \) flowing through it. - The loop is aligned with the coordinate planes such that: - One surface is parallel to the xz-plane. - Another surface is parallel to the yz-plane. - The loop creates a rectangular circuit and the dimensions of the rectangle are given as 'a' for both length and width. Arrows indicate the direction of the current steadily flowing through the loop: - \(\hat{x}\): The positive x-direction arrow indicates the current flowing parallel to the x-axis. - \(\hat{y}\): The positive y-direction arrow indicates the current is flowing parallel to the y-axis. - \(\hat{z}\): The current is flowing parallel to the z-axis. Use the right-hand rule: Point the thumb of your right hand in the direction of the current. The curl of your fingers indicates the direction of the magnetic dipole moment (\( \vec{\mu} \)). The formula for the magnetic dipole moment \( \vec{\mu} \) of a current loop is: \[ \vec{\mu} = I \cdot (\text{Area Vector}) \] Calculating the Area Vector: If we look closely, the loop is perpendicular to the plane forming a rectangle. The effective area vectors are the summ
Expert Solution
steps

Step by step

Solved in 3 steps with 4 images

Blurred answer
Knowledge Booster
Magnetic force
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON