(a) A 200-turn circular loop of radius 50.0 cm is vertical, with its axis on an east-west line. A current of 100 A circulates clockwise in the loop when viewed from the east. Earth's field here is due north, parallel to the ground, with a strength of 3.0×10−5T. What are the direction and magnitude of the torque on the loop? (b) Does this device have any practical applications as a motor?
(a) A 200-turn circular loop of radius 50.0 cm is vertical, with its axis on an east-west line. A current of 100 A circulates clockwise in the loop when viewed from the east. Earth's field here is due north, parallel to the ground, with a strength of 3.0×10−5T. What are the direction and magnitude of the torque on the loop? (b) Does this device have any practical applications as a motor?
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46) (a) A 200-turn circular loop of radius 50.0 cm is vertical, with its axis on an east-west line. A current of 100 A circulates clockwise in the loop when viewed from the east. Earth's field here is due north, parallel to the ground, with a strength of 3.0×10−5T. What are the direction and magnitude of the torque on the loop? (b) Does this device have any practical applications as a motor?
Please show actual values, equations, and drawings
![### Physics Problem Solving Exercise
**Problem Context:**
We are given the following variables:
- \( N = 200 \) (number of turns)
- \( R = 0.5 \, \text{m} \) (radius)
- \( I = 100 \, \text{A} \) (current)
- \( B = 3 \times 10^{-5} \, \text{T} \) (magnetic field)
We need to find the torque \( \tau \).
**Diagram Explanation:**
The diagram shows a loop with current \( I \), within a magnetic field \( \vec{B} \). The loop appears to be at an angle \( \theta = 30^\circ \). Vectors \( \vec{A} \) and \( \vec{B} \) are represented, along with directional angles.
**Equations and Solution:**
1. Torque is calculated using the cross product:
\[
\vec{\tau} = \vec{I} \times \vec{A} \times \vec{B}
\]
2. The magnitude of the torque \( |\vec{\tau}| \) is given by:
\[
|\vec{\tau}| = I |\vec{A}| |\vec{B}| \sin \theta
\]
3. Area vector magnitude \( |\vec{A}| \) for a circular loop is:
\[
|\vec{A}| = N \pi R^2
\]
4. Substituting values:
\[
|\vec{\tau}| = 100A \times 200 \times \pi \times (0.5 \, \text{m})^2 \times 3 \times 10^{-5} \, \text{T} \times \sin 30^\circ
\]
5. Calculate \( |\vec{E}| \), where the next step in the problem seems to involve an electric field or related quantity.
### Additional Notes:
- \( \theta = 30^\circ \) is crucial for solving the torque because it determines the angle at which the sinusoidal function (sin) will be applied.
- The product \( N \pi R^2 \) gives the total area of all loops considering the number of turns.
This problem involves vector analysis and use of trigonometric functions in physics](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F183a4de2-60b8-4988-9fb9-0a70f8d6fd02%2F69a1b71e-fca1-429e-83c0-cc34e0c4b6bf%2Fhce15al_processed.png&w=3840&q=75)
Transcribed Image Text:### Physics Problem Solving Exercise
**Problem Context:**
We are given the following variables:
- \( N = 200 \) (number of turns)
- \( R = 0.5 \, \text{m} \) (radius)
- \( I = 100 \, \text{A} \) (current)
- \( B = 3 \times 10^{-5} \, \text{T} \) (magnetic field)
We need to find the torque \( \tau \).
**Diagram Explanation:**
The diagram shows a loop with current \( I \), within a magnetic field \( \vec{B} \). The loop appears to be at an angle \( \theta = 30^\circ \). Vectors \( \vec{A} \) and \( \vec{B} \) are represented, along with directional angles.
**Equations and Solution:**
1. Torque is calculated using the cross product:
\[
\vec{\tau} = \vec{I} \times \vec{A} \times \vec{B}
\]
2. The magnitude of the torque \( |\vec{\tau}| \) is given by:
\[
|\vec{\tau}| = I |\vec{A}| |\vec{B}| \sin \theta
\]
3. Area vector magnitude \( |\vec{A}| \) for a circular loop is:
\[
|\vec{A}| = N \pi R^2
\]
4. Substituting values:
\[
|\vec{\tau}| = 100A \times 200 \times \pi \times (0.5 \, \text{m})^2 \times 3 \times 10^{-5} \, \text{T} \times \sin 30^\circ
\]
5. Calculate \( |\vec{E}| \), where the next step in the problem seems to involve an electric field or related quantity.
### Additional Notes:
- \( \theta = 30^\circ \) is crucial for solving the torque because it determines the angle at which the sinusoidal function (sin) will be applied.
- The product \( N \pi R^2 \) gives the total area of all loops considering the number of turns.
This problem involves vector analysis and use of trigonometric functions in physics
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