Référ to diagram 3. A vertical circular coil with 32 turns of radius 7.81 cm is free to rotate about a frictionless, horizontal axis through the center. Mass 6.77 kg hangs from the bottom of the coil; assume the coil's mass is negligible. The entire region is immersed in a uniform magnetic field of magnitude 0.695 T pointing downward. Now a switch is closed, and current 8 A flows in the coil. Find T, the magnitude of the net torque exerted on the loop just as the current begins, in N-m.
Référ to diagram 3. A vertical circular coil with 32 turns of radius 7.81 cm is free to rotate about a frictionless, horizontal axis through the center. Mass 6.77 kg hangs from the bottom of the coil; assume the coil's mass is negligible. The entire region is immersed in a uniform magnetic field of magnitude 0.695 T pointing downward. Now a switch is closed, and current 8 A flows in the coil. Find T, the magnitude of the net torque exerted on the loop just as the current begins, in N-m.
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Transcribed Image Text:**Diagram 3: Just as the coil is turned on**
**Description:**
- **Side View:**
- The diagram shows a vertical arrangement with the coil represented by a thin, oval shape. A small mass labeled "m" is suspended below the coil.
- **Front View:**
- The diagram depicts a circle representing the front view of the coil. The horizontal line across the circle is marked as the "axis." A small mass labeled "m" is again shown suspended below the coil.
This diagram illustrates the position and orientation of the coil and mass when the coil is activated.
![**Physics Problem: Rotating Coil in a Magnetic Field**
*Refer to diagram 3.*
A vertical circular coil with 32 turns and a radius of 7.81 cm is free to rotate about a frictionless, horizontal axis through its center. A mass of 6.77 kg hangs from the bottom of the coil, and the coil's mass is assumed to be negligible. The entire region is immersed in a uniform magnetic field with a magnitude of 0.695 T, pointing downward.
When a switch is closed, a current of 8 A begins to flow in the coil. Calculate \( \tau \), the magnitude of the net torque exerted on the loop, just as the current begins, in N·m.
**Explanation:**
- The coil is subject to a magnetic force due to the current and the magnetic field, which results in torque.
- Torque (\( \tau \)) is calculated using the formula:
\[
\tau = n \cdot I \cdot A \cdot B \cdot \sin(\theta)
\]
where:
- \( n \) = number of turns in the coil (32),
- \( I \) = current (8 A),
- \( A \) = area of the coil (\( \pi \cdot r^2 \), where \( r \) is the radius),
- \( B \) = magnetic field strength (0.695 T),
- \( \theta \) = angle between the normal to the coil and the magnetic field direction (90° since the field is vertical and initially the coil is horizontal).
- The task is to find the net torque when the current is first initiated.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdeb38e25-f570-4fb2-8928-75af9ed123c1%2F87309f53-c800-4a62-bcb3-5b0afe1cfd80%2Fxywlbh_processed.png&w=3840&q=75)
Transcribed Image Text:**Physics Problem: Rotating Coil in a Magnetic Field**
*Refer to diagram 3.*
A vertical circular coil with 32 turns and a radius of 7.81 cm is free to rotate about a frictionless, horizontal axis through its center. A mass of 6.77 kg hangs from the bottom of the coil, and the coil's mass is assumed to be negligible. The entire region is immersed in a uniform magnetic field with a magnitude of 0.695 T, pointing downward.
When a switch is closed, a current of 8 A begins to flow in the coil. Calculate \( \tau \), the magnitude of the net torque exerted on the loop, just as the current begins, in N·m.
**Explanation:**
- The coil is subject to a magnetic force due to the current and the magnetic field, which results in torque.
- Torque (\( \tau \)) is calculated using the formula:
\[
\tau = n \cdot I \cdot A \cdot B \cdot \sin(\theta)
\]
where:
- \( n \) = number of turns in the coil (32),
- \( I \) = current (8 A),
- \( A \) = area of the coil (\( \pi \cdot r^2 \), where \( r \) is the radius),
- \( B \) = magnetic field strength (0.695 T),
- \( \theta \) = angle between the normal to the coil and the magnetic field direction (90° since the field is vertical and initially the coil is horizontal).
- The task is to find the net torque when the current is first initiated.
Expert Solution
Step 1
Given:
The number of turns in the coil are .
The radius of the coil is .
The mass of the object that hangs from the coil is .
The magnitude of the magnetic field is .
The current flowing through the coil is .
Introduction:
Torque is the measure of the force that can cause an object to rotate about an axis. Force is what causes an object to accelerate in linear kinematics. Similarly, torque is what causes an angular acceleration. Hence, torque can be defined as the rotational equivalent of linear force. It is also known as the moment of force.
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