A rectangular loop of wire of width 10 cm and lengut 20 cn has a current of 2.5 A flowing through it Two sides of the loop are oriented parallel to a unirorm magnetic field of strength 0.037 T, the other two sides being perpendicular to the magnetic field. The magnitude of the torque on the loop is A) 0.025 m-N. B) 0.0093 m-N. C) 0.038 m-N. D) 0.0019 m-N. E) 0.050 m-N.
A rectangular loop of wire of width 10 cm and lengut 20 cn has a current of 2.5 A flowing through it Two sides of the loop are oriented parallel to a unirorm magnetic field of strength 0.037 T, the other two sides being perpendicular to the magnetic field. The magnitude of the torque on the loop is A) 0.025 m-N. B) 0.0093 m-N. C) 0.038 m-N. D) 0.0019 m-N. E) 0.050 m-N.
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Chapter1: Units, Trigonometry. And Vectors
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![### Problem Statement
A rectangular loop of wire of width 10 cm and length 20 cm has a current of 2.5 A flowing through it. Two sides of the loop are oriented parallel to a uniform magnetic field of strength 0.037 T, with the other two sides being perpendicular to the magnetic field. The magnitude of the torque on the loop is:
#### Options
A) 0.025 m⋅N
B) 0.0093 m⋅N
C) 0.038 m⋅N
D) 0.0019 m⋅N
E) 0.050 m⋅N
### Explanation
To solve for the torque on a rectangular loop in a magnetic field, the equation used is:
\[ \tau = n \cdot I \cdot A \cdot B \cdot \sin(\theta) \]
Where:
- \( \tau \) is the torque,
- \( n \) is the number of loops (1 in this case),
- \( I \) is the current (2.5 A),
- \( A \) is the area of the loop,
- \( B \) is the magnetic field strength (0.037 T),
- \( \theta \) is the angle between the normal to the plane of the loop and the magnetic field (90 degrees here, so \(\sin(90^\circ) = 1\)).
Given the width = 10 cm = 0.1 m and the length = 20 cm = 0.2 m, the area \( A \) becomes \( 0.1 \times 0.2 = 0.02 \, \text{m}^2 \).
Plug these values into the formula to find the torque.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fda546acf-142d-4ad9-8d8a-e789891e6e32%2F63b4beec-9da9-467e-8560-953624eaba32%2Fo86gg06_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
A rectangular loop of wire of width 10 cm and length 20 cm has a current of 2.5 A flowing through it. Two sides of the loop are oriented parallel to a uniform magnetic field of strength 0.037 T, with the other two sides being perpendicular to the magnetic field. The magnitude of the torque on the loop is:
#### Options
A) 0.025 m⋅N
B) 0.0093 m⋅N
C) 0.038 m⋅N
D) 0.0019 m⋅N
E) 0.050 m⋅N
### Explanation
To solve for the torque on a rectangular loop in a magnetic field, the equation used is:
\[ \tau = n \cdot I \cdot A \cdot B \cdot \sin(\theta) \]
Where:
- \( \tau \) is the torque,
- \( n \) is the number of loops (1 in this case),
- \( I \) is the current (2.5 A),
- \( A \) is the area of the loop,
- \( B \) is the magnetic field strength (0.037 T),
- \( \theta \) is the angle between the normal to the plane of the loop and the magnetic field (90 degrees here, so \(\sin(90^\circ) = 1\)).
Given the width = 10 cm = 0.1 m and the length = 20 cm = 0.2 m, the area \( A \) becomes \( 0.1 \times 0.2 = 0.02 \, \text{m}^2 \).
Plug these values into the formula to find the torque.
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