Two concentric, circular wire loops of radii r = 26.8 cm and r2 = 55.0 cm, are located in an xy plane; each carries a clockwise current of 6.44 A (see the figure below). (a) Find the magnitude of the net magnetic dipole moment of the system. (b) Repeat for reversed current in the inner loop. 12 (a) Number i Units Units (b) Number
Two concentric, circular wire loops of radii r = 26.8 cm and r2 = 55.0 cm, are located in an xy plane; each carries a clockwise current of 6.44 A (see the figure below). (a) Find the magnitude of the net magnetic dipole moment of the system. (b) Repeat for reversed current in the inner loop. 12 (a) Number i Units Units (b) Number
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8b65224-21df-49da-a8da-84f6a1af571d%2Fbd137553-3208-4bfd-845b-3a89edcb14f3%2Fpi2rlvi_processed.jpeg&w=3840&q=75)
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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