A uniform magnetic field passes through a horizontal circular wire loop at an angle 15.1° from the normal to the plane of the loop. The magnitude of the magnetic field is 3.35 T, and the radius of the wire loop is 0.230 m. Find the magnetic flux O through the loop.
A uniform magnetic field passes through a horizontal circular wire loop at an angle 15.1° from the normal to the plane of the loop. The magnitude of the magnetic field is 3.35 T, and the radius of the wire loop is 0.230 m. Find the magnetic flux O through the loop.
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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![**Problem Statement:**
A uniform magnetic field passes through a horizontal circular wire loop at an angle of \(15.1^\circ\) from the normal to the plane of the loop. The magnitude of the magnetic field is \(3.35 \, \text{T}\), and the radius of the wire loop is \(0.230 \, \text{m}\). Find the magnetic flux \(\Phi\) through the loop.
\[
\Phi = \, \boxed{\phantom{0000}} \, \text{Wb}
\]
**Diagram Explanation:**
The diagram shows a circular wire loop, depicted as an orange circle, with blue arrows passing through it. These arrows represent the direction of the magnetic field lines. The arrows are oriented at an angle, indicating that the magnetic field is not perpendicular to the plane of the loop but instead forms an angle of \(15.1^\circ\) with the normal to the plane.
**Concepts to Consider:**
- **Magnetic Flux (\(\Phi\)):** This is the measure of the amount of magnetic field passing through a given area.
- **Formula for Magnetic Flux:**
\[
\Phi = B \cdot A \cdot \cos(\theta)
\]
where \(B\) is the magnetic field strength, \(A\) is the area of the loop, and \(\theta\) is the angle between the magnetic field lines and the normal to the plane of the loop.
- **Area of the Circle (\(A\)):**
\[
A = \pi r^2
\]
where \(r\) is the radius of the circle.
In this problem, use the given values to find the magnetic flux through the loop.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F159d614f-facc-4d4c-a1ed-1d4b6c60e1d9%2F4c1e7b9f-4dcf-414a-80d3-ee0f40636691%2Fbp0oxe_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A uniform magnetic field passes through a horizontal circular wire loop at an angle of \(15.1^\circ\) from the normal to the plane of the loop. The magnitude of the magnetic field is \(3.35 \, \text{T}\), and the radius of the wire loop is \(0.230 \, \text{m}\). Find the magnetic flux \(\Phi\) through the loop.
\[
\Phi = \, \boxed{\phantom{0000}} \, \text{Wb}
\]
**Diagram Explanation:**
The diagram shows a circular wire loop, depicted as an orange circle, with blue arrows passing through it. These arrows represent the direction of the magnetic field lines. The arrows are oriented at an angle, indicating that the magnetic field is not perpendicular to the plane of the loop but instead forms an angle of \(15.1^\circ\) with the normal to the plane.
**Concepts to Consider:**
- **Magnetic Flux (\(\Phi\)):** This is the measure of the amount of magnetic field passing through a given area.
- **Formula for Magnetic Flux:**
\[
\Phi = B \cdot A \cdot \cos(\theta)
\]
where \(B\) is the magnetic field strength, \(A\) is the area of the loop, and \(\theta\) is the angle between the magnetic field lines and the normal to the plane of the loop.
- **Area of the Circle (\(A\)):**
\[
A = \pi r^2
\]
where \(r\) is the radius of the circle.
In this problem, use the given values to find the magnetic flux through the loop.
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