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Uniform magnetic field exist in a region is that greater than zero in minus z cap direction a conducting semi circular close loop of radius a lies in magnetic field with its centre at 0 0 if loop is to be rotated with angular speed Omega about z Axis then magnitude of torse required is?
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Uniform magnetic field exist in a region is that greater than zero in ...
Introduction
To analyze the situation of a conducting semi-circular loop in a uniform magnetic field, we need to determine the torque required to maintain its rotation about the z-axis.
Magnetic Field and Loop Orientation
- The magnetic field is directed in the negative z-direction (B = -Bz hat).
- The semi-circular loop lies in the xy-plane, centered at the origin (0,0).
Induced EMF
- As the loop rotates with angular speed \( \Omega \), it experiences a change in magnetic flux.
- The induced electromotive force (EMF) in the loop can be calculated using Faraday's law:
\[ \text{EMF} = -\frac{d\Phi}{dt} \]
- The magnetic flux \( \Phi \) through the loop is given by:
\[ \Phi = B \cdot A \]
- As the loop rotates, the area \( A \) exposed to the magnetic field changes, inducing an EMF in the loop.
Current and Torque Calculation
- The induced EMF generates a current \( I \) in the loop, which can be calculated using Ohm's law:
\[ I = \frac{\text{EMF}}{R} \]
where \( R \) is the resistance of the loop.
- The torque \( \tau \) acting on the loop due to the magnetic field is given by:
\[ \tau = I \cdot A \cdot B \]
where \( A \) is the area vector of the loop, directed along the normal to the plane of the loop.
Magnitude of Torque Required
- The magnitude of the torque required to maintain the rotation can thus be expressed as:
\[ \tau = \frac{(B \cdot A)}{R} \cdot A \cdot B \]
- Plugging in the values of \( A \) and \( B \), we can derive the specific torque required to counteract the forces acting on the loop during its rotation in the magnetic field.
This torque ensures that the loop continues to rotate at the desired angular speed \( \Omega \).
To analyze the situation of a conducting semi-circular loop in a uniform magnetic field, we need to determine the torque required to maintain its rotation about the z-axis.
Magnetic Field and Loop Orientation
- The magnetic field is directed in the negative z-direction (B = -Bz hat).
- The semi-circular loop lies in the xy-plane, centered at the origin (0,0).
Induced EMF
- As the loop rotates with angular speed \( \Omega \), it experiences a change in magnetic flux.
- The induced electromotive force (EMF) in the loop can be calculated using Faraday's law:
\[ \text{EMF} = -\frac{d\Phi}{dt} \]
- The magnetic flux \( \Phi \) through the loop is given by:
\[ \Phi = B \cdot A \]
- As the loop rotates, the area \( A \) exposed to the magnetic field changes, inducing an EMF in the loop.
Current and Torque Calculation
- The induced EMF generates a current \( I \) in the loop, which can be calculated using Ohm's law:
\[ I = \frac{\text{EMF}}{R} \]
where \( R \) is the resistance of the loop.
- The torque \( \tau \) acting on the loop due to the magnetic field is given by:
\[ \tau = I \cdot A \cdot B \]
where \( A \) is the area vector of the loop, directed along the normal to the plane of the loop.
Magnitude of Torque Required
- The magnitude of the torque required to maintain the rotation can thus be expressed as:
\[ \tau = \frac{(B \cdot A)}{R} \cdot A \cdot B \]
- Plugging in the values of \( A \) and \( B \), we can derive the specific torque required to counteract the forces acting on the loop during its rotation in the magnetic field.
This torque ensures that the loop continues to rotate at the desired angular speed \( \Omega \).
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Uniform magnetic field exist in a region is that greater than zero in minus z cap direction a conducting semi circular close loop of radius a lies in magnetic field with its centre at 0 0 if loop is to be rotated with angular speed Omega about z Axis then magnitude of torse required is?
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Uniform magnetic field exist in a region is that greater than zero in minus z cap direction a conducting semi circular close loop of radius a lies in magnetic field with its centre at 0 0 if loop is to be rotated with angular speed Omega about z Axis then magnitude of torse required is? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Uniform magnetic field exist in a region is that greater than zero in minus z cap direction a conducting semi circular close loop of radius a lies in magnetic field with its centre at 0 0 if loop is to be rotated with angular speed Omega about z Axis then magnitude of torse required is? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Uniform magnetic field exist in a region is that greater than zero in minus z cap direction a conducting semi circular close loop of radius a lies in magnetic field with its centre at 0 0 if loop is to be rotated with angular speed Omega about z Axis then magnitude of torse required is?.
Uniform magnetic field exist in a region is that greater than zero in minus z cap direction a conducting semi circular close loop of radius a lies in magnetic field with its centre at 0 0 if loop is to be rotated with angular speed Omega about z Axis then magnitude of torse required is? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Uniform magnetic field exist in a region is that greater than zero in minus z cap direction a conducting semi circular close loop of radius a lies in magnetic field with its centre at 0 0 if loop is to be rotated with angular speed Omega about z Axis then magnitude of torse required is? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Uniform magnetic field exist in a region is that greater than zero in minus z cap direction a conducting semi circular close loop of radius a lies in magnetic field with its centre at 0 0 if loop is to be rotated with angular speed Omega about z Axis then magnitude of torse required is?.
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