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A uniform magnetic field B -zcap exist in the region x>0 a conducting semi circular closed loop of radius 'a' lies in magnetic field with its centre at origin if the loop is to be rotated with angular speed omega about z axis then magnitude of torque required is please solve with calculation also?
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A uniform magnetic field B -zcap exist in the region x>0 a conducting ...
Understanding the Problem
To determine the torque needed to rotate a conducting semi-circular loop in a uniform magnetic field, we start by understanding the interaction between the loop and the magnetic field. The loop is placed in a magnetic field directed along the negative z-axis (B = -z cap), and it rotates about the z-axis.
Magnetic Moment of the Loop
- The magnetic moment (μ) of a current-carrying loop is given by the formula:
μ = I * A
where 'I' is the current flowing through the loop, and 'A' is the area vector of the loop.
- For a semi-circular loop of radius 'a':
A = (1/2) * π * a^2
Thus, the magnetic moment will be:
μ = I * (1/2) * π * a^2
Torque on the Loop
- The torque (τ) experienced by the loop in a magnetic field is given by:
τ = μ × B
Since B is along the negative z-axis, the torque will act in the x-y plane.
- The magnitude of torque is:
τ = μ * B * sin(θ)
Here, θ is the angle between μ and B. When the loop rotates, θ remains 90 degrees.
- Therefore, τ = μ * B.
Substituting Values
- Substitute μ and B into the torque equation:
τ = (I * (1/2) * π * a^2) * |B|
where |B| is the magnitude of the magnetic field.
Final Expression for Torque
- Thus, the required torque to maintain the rotation of the loop is:
τ = (I * (1/2) * π * a^2) * |B|
This equation describes the torque needed to keep the conducting semi-circular loop rotating in the presence of a uniform magnetic field.
To determine the torque needed to rotate a conducting semi-circular loop in a uniform magnetic field, we start by understanding the interaction between the loop and the magnetic field. The loop is placed in a magnetic field directed along the negative z-axis (B = -z cap), and it rotates about the z-axis.
Magnetic Moment of the Loop
- The magnetic moment (μ) of a current-carrying loop is given by the formula:
μ = I * A
where 'I' is the current flowing through the loop, and 'A' is the area vector of the loop.
- For a semi-circular loop of radius 'a':
A = (1/2) * π * a^2
Thus, the magnetic moment will be:
μ = I * (1/2) * π * a^2
Torque on the Loop
- The torque (τ) experienced by the loop in a magnetic field is given by:
τ = μ × B
Since B is along the negative z-axis, the torque will act in the x-y plane.
- The magnitude of torque is:
τ = μ * B * sin(θ)
Here, θ is the angle between μ and B. When the loop rotates, θ remains 90 degrees.
- Therefore, τ = μ * B.
Substituting Values
- Substitute μ and B into the torque equation:
τ = (I * (1/2) * π * a^2) * |B|
where |B| is the magnitude of the magnetic field.
Final Expression for Torque
- Thus, the required torque to maintain the rotation of the loop is:
τ = (I * (1/2) * π * a^2) * |B|
This equation describes the torque needed to keep the conducting semi-circular loop rotating in the presence of a uniform magnetic field.
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A uniform magnetic field B -zcap exist in the region x>0 a conducting semi circular closed loop of radius 'a' lies in magnetic field with its centre at origin if the loop is to be rotated with angular speed omega about z axis then magnitude of torque required is please solve with calculation also?
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A uniform magnetic field B -zcap exist in the region x>0 a conducting semi circular closed loop of radius 'a' lies in magnetic field with its centre at origin if the loop is to be rotated with angular speed omega about z axis then magnitude of torque required is please solve with calculation also? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A uniform magnetic field B -zcap exist in the region x>0 a conducting semi circular closed loop of radius 'a' lies in magnetic field with its centre at origin if the loop is to be rotated with angular speed omega about z axis then magnitude of torque required is please solve with calculation also? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A uniform magnetic field B -zcap exist in the region x>0 a conducting semi circular closed loop of radius 'a' lies in magnetic field with its centre at origin if the loop is to be rotated with angular speed omega about z axis then magnitude of torque required is please solve with calculation also?.
A uniform magnetic field B -zcap exist in the region x>0 a conducting semi circular closed loop of radius 'a' lies in magnetic field with its centre at origin if the loop is to be rotated with angular speed omega about z axis then magnitude of torque required is please solve with calculation also? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A uniform magnetic field B -zcap exist in the region x>0 a conducting semi circular closed loop of radius 'a' lies in magnetic field with its centre at origin if the loop is to be rotated with angular speed omega about z axis then magnitude of torque required is please solve with calculation also? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A uniform magnetic field B -zcap exist in the region x>0 a conducting semi circular closed loop of radius 'a' lies in magnetic field with its centre at origin if the loop is to be rotated with angular speed omega about z axis then magnitude of torque required is please solve with calculation also?.
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