(L10) A single circular current-carrying loop 4.40E-2 m in radius is centered at the origin and carries a current of 2.71 A so that its magnetic moment u points at an angle 27.0° from the +y axis, as shown. A uniform, constant magnetic field B 0.544 T is applied in the ty direction. What is the magnitude of torque that the magnetic field exerts on the current loop (in N-m)? +y B 0 que +x =
(L10) A single circular current-carrying loop 4.40E-2 m in radius is centered at the origin and carries a current of 2.71 A so that its magnetic moment u points at an angle 27.0° from the +y axis, as shown. A uniform, constant magnetic field B 0.544 T is applied in the ty direction. What is the magnitude of torque that the magnetic field exerts on the current loop (in N-m)? +y B 0 que +x =
Transcribed Image Text:**Problem Statement (L10)**
A single circular current-carrying loop with a radius of \(4.40 \times 10^{-2}\) meters is centered at the origin and carries a current of 2.71 amperes. The magnetic moment \(\mu\) of the loop points at an angle \(\theta = 27.0^\circ\) from the \(+y\)-axis, as shown in the diagram. A uniform, constant magnetic field \(B = 0.544\) teslas is applied in the \(+y\) direction.
**Question:** What is the magnitude of the torque that the magnetic field exerts on the current loop (in Newton-meters, N⋅m)?
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**Diagram Explanation:**
The accompanying vector diagram illustrates the relationship between the magnetic moment \(\mu\), the magnetic field \(B\), and the angle \(\theta\):
- The vertical arrow labeled \(B\) represents the direction of the magnetic field, aligned with the \(+y\)-axis.
- The vector labeled \(\mu\) represents the magnetic moment of the loop and lies at an angle \(\theta\) (\(27.0^\circ\)) from the \(+y\)-axis.
- The loop’s orientation is indicated by a circle in the \(xy\)-plane at the origin.
- The coordinate axes (\(+x\) and \(+y\)) are also indicated for reference.
---
**Solution Approach:**
To determine the magnitude of torque (\(\tau\)) exerted by the magnetic field on the current loop, we use the formula:
\[
\tau = \mu B \sin \theta
\]
where:
- \(\mu\) is the magnetic moment of the loop,
- \(B\) is the magnetic field strength,
- \(\theta\) is the angle between \(\mu\) and \(B\).
The magnetic moment \(\mu\) for a current loop is given by:
\[
\mu = I \cdot A
\]
where:
- \(I\) is the current,
- \(A\) is the area of the loop.
The area \(A\) of a circular loop is:
\[
A = \pi r^2
\]
Given values:
- Current \(I = 2.71\) A,
- Radius of the loop \(r = 4.
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![**Problem Statement (L10)**
A single circular current-carrying loop with a radius of \(4.40 \times 10^{-2}\) meters is centered at the origin and carries a current of 2.71 amperes. The magnetic moment \(\mu\) of the loop points at an angle \(\theta = 27.0^\circ\) from the \(+y\)-axis, as shown in the diagram. A uniform, constant magnetic field \(B = 0.544\) teslas is applied in the \(+y\) direction.
**Question:** What is the magnitude of the torque that the magnetic field exerts on the current loop (in Newton-meters, N⋅m)?
---
**Diagram Explanation:**
The accompanying vector diagram illustrates the relationship between the magnetic moment \(\mu\), the magnetic field \(B\), and the angle \(\theta\):
- The vertical arrow labeled \(B\) represents the direction of the magnetic field, aligned with the \(+y\)-axis.
- The vector labeled \(\mu\) represents the magnetic moment of the loop and lies at an angle \(\theta\) (\(27.0^\circ\)) from the \(+y\)-axis.
- The loop’s orientation is indicated by a circle in the \(xy\)-plane at the origin.
- The coordinate axes (\(+x\) and \(+y\)) are also indicated for reference.
---
**Solution Approach:**
To determine the magnitude of torque (\(\tau\)) exerted by the magnetic field on the current loop, we use the formula:
\[
\tau = \mu B \sin \theta
\]
where:
- \(\mu\) is the magnetic moment of the loop,
- \(B\) is the magnetic field strength,
- \(\theta\) is the angle between \(\mu\) and \(B\).
The magnetic moment \(\mu\) for a current loop is given by:
\[
\mu = I \cdot A
\]
where:
- \(I\) is the current,
- \(A\) is the area of the loop.
The area \(A\) of a circular loop is:
\[
A = \pi r^2
\]
Given values:
- Current \(I = 2.71\) A,
- Radius of the loop \(r = 4.](https://content.bartleby.com/qna-images/question/6401e82b-1884-43b6-8725-0773860dca12/0e1ac701-f60f-4554-b6b7-f94d394d3017/v2icdmp_processed.png)
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