College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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### Finding the Net Magnetic Dipole Moment of Concentric Circular Wire Loops

**Problem Statement:**
Two concentric, circular wire loops of radii \( r_1 = 26.8 \) cm and \( r_2 = 55.0 \) cm, are located in an xy plane; each carries a clockwise current of 6.44 A (see the figure below). 

**Tasks:**
(a) Find the magnitude of the net magnetic dipole moment of the system.
(b) Repeat for reversed current in the inner loop.

**Diagram:**
A figure is provided which depicts two concentric circular wire loops situated in the xy plane. The outer loop has a radius \( r_2 \) and the inner loop has a radius \( r_1 \). Both loops carry a current \( i \) in a clockwise direction, as indicated by the arrows.

#### Calculation Details:

1. **Determine the Magnetic Dipole Moment for Each Loop:**
   - The magnetic dipole moment \( \mu \) for a single loop of current-carrying wire is given by:
     \[
     \mu = I \cdot A
     \]
     where \( I \) is the current and \( A \) is the area of the loop.

2. **Calculate the Area for Each Loop:**
   - For the inner loop, area \( A_1 \) is:
     \[
     A_1 = \pi r_1^2
     \]
   - For the outer loop, area \( A_2 \) is:
     \[
     A_2 = \pi r_2^2
     \]

3. **Compute the Magnetic Dipole Moments:**
   - For the inner loop:
     \[
     \mu_1 = I \cdot A_1 = 6.44 \, \text{A} \cdot \pi (0.268 \, \text{m})^2
     \]
   - For the outer loop:
     \[
     \mu_2 = I \cdot A_2 = 6.44 \, \text{A} \cdot \pi (0.55 \, \text{m})^2
     \]

4. **Determine the Net Magnetic Dipole Moment:**
   - Since both currents are in the same direction (clockwise), the net magnetic dipole moment is
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Transcribed Image Text:### Finding the Net Magnetic Dipole Moment of Concentric Circular Wire Loops **Problem Statement:** Two concentric, circular wire loops of radii \( r_1 = 26.8 \) cm and \( r_2 = 55.0 \) cm, are located in an xy plane; each carries a clockwise current of 6.44 A (see the figure below). **Tasks:** (a) Find the magnitude of the net magnetic dipole moment of the system. (b) Repeat for reversed current in the inner loop. **Diagram:** A figure is provided which depicts two concentric circular wire loops situated in the xy plane. The outer loop has a radius \( r_2 \) and the inner loop has a radius \( r_1 \). Both loops carry a current \( i \) in a clockwise direction, as indicated by the arrows. #### Calculation Details: 1. **Determine the Magnetic Dipole Moment for Each Loop:** - The magnetic dipole moment \( \mu \) for a single loop of current-carrying wire is given by: \[ \mu = I \cdot A \] where \( I \) is the current and \( A \) is the area of the loop. 2. **Calculate the Area for Each Loop:** - For the inner loop, area \( A_1 \) is: \[ A_1 = \pi r_1^2 \] - For the outer loop, area \( A_2 \) is: \[ A_2 = \pi r_2^2 \] 3. **Compute the Magnetic Dipole Moments:** - For the inner loop: \[ \mu_1 = I \cdot A_1 = 6.44 \, \text{A} \cdot \pi (0.268 \, \text{m})^2 \] - For the outer loop: \[ \mu_2 = I \cdot A_2 = 6.44 \, \text{A} \cdot \pi (0.55 \, \text{m})^2 \] 4. **Determine the Net Magnetic Dipole Moment:** - Since both currents are in the same direction (clockwise), the net magnetic dipole moment is
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