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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(0,0,0), if the loop is to be rotated with angular speed omega about z axis then magnitude of torque required is?
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A uniform magnetic field B(-zcap) exist in the region x>0, a conductin...
Understanding the System
The system consists of a conducting semi-circular loop placed in a uniform magnetic field directed along the negative z-axis (B = -Bz). The loop has a radius 'a' and is centered at the origin (0,0,0).
Induced EMF and Current
When the loop rotates with an angular speed omega about the z-axis, it cuts through the magnetic field lines, leading to an induced electromotive force (EMF) according to Faraday's law of electromagnetic induction. The induced EMF (ε) can be calculated using:
- ε = -dΦ/dt
Where Φ is the magnetic flux through the loop.
Magnetic Flux Calculation
The magnetic flux (Φ) through the semi-circular loop is given by:
- Φ = B * A = B * (1/2) * π * a^2
Here, A is the area of the semi-circle.
As the loop rotates, the area vector changes, leading to a change in flux, which induces current in the loop.
Torque on the Loop
The torque (τ) acting on the loop due to the magnetic field can be expressed as:
- τ = μ x B
Where μ (magnetic moment) for the loop is given by:
- μ = I * A
I is the current flowing through the loop, and A is the area vector of the loop.
Magnitude of Torque Required
The magnitude of the torque required to maintain the rotation can be derived as follows:
1. Calculate the induced current (I) using Ohm's law considering resistance (R) of the loop.
2. Substitute I into μ = I * (1/2) * π * a^2.
3. Finally, compute τ = μ * B.
The expression for torque simplifies to:
- τ = (I * (1/2) * π * a^2) * B
This represents the torque needed to keep the loop rotating in the magnetic field.
Conclusion
The required torque is essential to counteract the effects of the magnetic field on the rotating loop and ensure continuous motion.
The system consists of a conducting semi-circular loop placed in a uniform magnetic field directed along the negative z-axis (B = -Bz). The loop has a radius 'a' and is centered at the origin (0,0,0).
Induced EMF and Current
When the loop rotates with an angular speed omega about the z-axis, it cuts through the magnetic field lines, leading to an induced electromotive force (EMF) according to Faraday's law of electromagnetic induction. The induced EMF (ε) can be calculated using:
- ε = -dΦ/dt
Where Φ is the magnetic flux through the loop.
Magnetic Flux Calculation
The magnetic flux (Φ) through the semi-circular loop is given by:
- Φ = B * A = B * (1/2) * π * a^2
Here, A is the area of the semi-circle.
As the loop rotates, the area vector changes, leading to a change in flux, which induces current in the loop.
Torque on the Loop
The torque (τ) acting on the loop due to the magnetic field can be expressed as:
- τ = μ x B
Where μ (magnetic moment) for the loop is given by:
- μ = I * A
I is the current flowing through the loop, and A is the area vector of the loop.
Magnitude of Torque Required
The magnitude of the torque required to maintain the rotation can be derived as follows:
1. Calculate the induced current (I) using Ohm's law considering resistance (R) of the loop.
2. Substitute I into μ = I * (1/2) * π * a^2.
3. Finally, compute τ = μ * B.
The expression for torque simplifies to:
- τ = (I * (1/2) * π * a^2) * B
This represents the torque needed to keep the loop rotating in the magnetic field.
Conclusion
The required torque is essential to counteract the effects of the magnetic field on the rotating loop and ensure continuous motion.
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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(0,0,0), if the loop is to be rotated with angular speed omega about z axis then magnitude of torque required is?
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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(0,0,0), if the loop is to be rotated with angular speed omega about z axis then magnitude of torque required is? 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(0,0,0), if the loop is to be rotated with angular speed omega about z axis then magnitude of torque required is? 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(0,0,0), if the loop is to be rotated with angular speed omega about z axis then magnitude of torque required is?.
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(0,0,0), if the loop is to be rotated with angular speed omega about z axis then magnitude of torque required is? 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(0,0,0), if the loop is to be rotated with angular speed omega about z axis then magnitude of torque required is? 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(0,0,0), if the loop is to be rotated with angular speed omega about z axis then magnitude of torque required is?.
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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(0,0,0), if the loop is to be rotated with angular speed omega about z axis then magnitude of torque required is?, a detailed solution 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(0,0,0), if the loop is to be rotated with angular speed omega about z axis then magnitude of torque required is? has been provided alongside types of 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(0,0,0), if the loop is to be rotated with angular speed omega about z axis then magnitude of torque required is? theory, EduRev gives you an
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