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Super conductig square rigid frame of mass m, self inductance L and side a is cooled down (in a magnetic field) to a temperature below the critical temperature. The frame is kept horizontal (parallel to the x-y plane) and constarined to move in the z- direction in a non - uniform but constant magnetic field given by →B=−αx^i+(αz+B0)^k and a uniform gravitational field given by accelaration −g^k as shown in figure. The thickness of the frame is much smaller than a. Initially the frame is at rest with its centre conciding with the origin. Now the frame is released at t=0.
Maximum magnitude of Z - cordinate of centre of loop during subsquent motion will be?
Maximum magnitude of Z - cordinate of centre of loop during subsquent motion will be?
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Super conductig square rigid frame of mass m, self inductance L and si...
Magnetic Field and Forces Acting on the Frame
The given magnetic field is expressed as:
→B = −αx^i + (αz + B0)^k
The frame, upon being released, experiences the following forces:
- **Magnetic Force**: Due to the motion of the superconducting frame in the magnetic field.
- **Gravitational Force**: Acts downward with an acceleration of −g^k.
Induced EMF and Motion
As the frame falls, it cuts through the magnetic field lines, inducing an electromotive force (EMF) due to Faraday’s Law of Electromagnetic Induction. This EMF generates a current in the frame, which interacts with the magnetic field, resulting in a magnetic force that opposes the motion (Lenz's Law).
Equation of Motion
The net force acting on the frame can be expressed as:
- **Net Force**: F_net = m(-g + B_induced)
Where B_induced is the magnetic force due to the induced current.
The frame will accelerate upwards due to the induced magnetic force until it reaches a point where gravitational force balances the upward magnetic force.
Maximum Z-coordinate Calculation
At the maximum height (Z_max), the upward force equals the gravitational force:
- **Condition**: B_induced = g
The induced magnetic force is proportional to the change in magnetic flux and the self-inductance (L) of the frame. The maximum height can be derived from the energy considerations or the balance of forces.
Using the properties of superconductors and the conservation of energy, the maximum height (Z_max) can be approximated as:
- **Z_max** = (L * B0) / (m * g)
Conclusion
The maximum magnitude of the Z-coordinate of the center of the loop during subsequent motion will be proportional to the self-inductance, the external magnetic field, and inversely proportional to the mass and gravitational acceleration. This showcases the intricate interplay between magnetic forces and gravitational effects in superconducting systems.
The given magnetic field is expressed as:
→B = −αx^i + (αz + B0)^k
The frame, upon being released, experiences the following forces:
- **Magnetic Force**: Due to the motion of the superconducting frame in the magnetic field.
- **Gravitational Force**: Acts downward with an acceleration of −g^k.
Induced EMF and Motion
As the frame falls, it cuts through the magnetic field lines, inducing an electromotive force (EMF) due to Faraday’s Law of Electromagnetic Induction. This EMF generates a current in the frame, which interacts with the magnetic field, resulting in a magnetic force that opposes the motion (Lenz's Law).
Equation of Motion
The net force acting on the frame can be expressed as:
- **Net Force**: F_net = m(-g + B_induced)
Where B_induced is the magnetic force due to the induced current.
The frame will accelerate upwards due to the induced magnetic force until it reaches a point where gravitational force balances the upward magnetic force.
Maximum Z-coordinate Calculation
At the maximum height (Z_max), the upward force equals the gravitational force:
- **Condition**: B_induced = g
The induced magnetic force is proportional to the change in magnetic flux and the self-inductance (L) of the frame. The maximum height can be derived from the energy considerations or the balance of forces.
Using the properties of superconductors and the conservation of energy, the maximum height (Z_max) can be approximated as:
- **Z_max** = (L * B0) / (m * g)
Conclusion
The maximum magnitude of the Z-coordinate of the center of the loop during subsequent motion will be proportional to the self-inductance, the external magnetic field, and inversely proportional to the mass and gravitational acceleration. This showcases the intricate interplay between magnetic forces and gravitational effects in superconducting systems.
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Super conductig square rigid frame of mass m, self inductance L and side a is cooled down (in a magnetic field) to a temperature below the critical temperature. The frame is kept horizontal (parallel to the x-y plane) and constarined to move in the z- direction in a non - uniform but constant magnetic field given by →B=−αx^i+(αz+B0)^k and a uniform gravitational field given by accelaration −g^k as shown in figure. The thickness of the frame is much smaller than a. Initially the frame is at rest with its centre conciding with the origin. Now the frame is released at t=0.Maximum magnitude of Z - cordinate of centre of loop during subsquent motion will be?
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Super conductig square rigid frame of mass m, self inductance L and side a is cooled down (in a magnetic field) to a temperature below the critical temperature. The frame is kept horizontal (parallel to the x-y plane) and constarined to move in the z- direction in a non - uniform but constant magnetic field given by →B=−αx^i+(αz+B0)^k and a uniform gravitational field given by accelaration −g^k as shown in figure. The thickness of the frame is much smaller than a. Initially the frame is at rest with its centre conciding with the origin. Now the frame is released at t=0.Maximum magnitude of Z - cordinate of centre of loop during subsquent motion will be? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Super conductig square rigid frame of mass m, self inductance L and side a is cooled down (in a magnetic field) to a temperature below the critical temperature. The frame is kept horizontal (parallel to the x-y plane) and constarined to move in the z- direction in a non - uniform but constant magnetic field given by →B=−αx^i+(αz+B0)^k and a uniform gravitational field given by accelaration −g^k as shown in figure. The thickness of the frame is much smaller than a. Initially the frame is at rest with its centre conciding with the origin. Now the frame is released at t=0.Maximum magnitude of Z - cordinate of centre of loop during subsquent motion will be? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Super conductig square rigid frame of mass m, self inductance L and side a is cooled down (in a magnetic field) to a temperature below the critical temperature. The frame is kept horizontal (parallel to the x-y plane) and constarined to move in the z- direction in a non - uniform but constant magnetic field given by →B=−αx^i+(αz+B0)^k and a uniform gravitational field given by accelaration −g^k as shown in figure. The thickness of the frame is much smaller than a. Initially the frame is at rest with its centre conciding with the origin. Now the frame is released at t=0.Maximum magnitude of Z - cordinate of centre of loop during subsquent motion will be?.
Super conductig square rigid frame of mass m, self inductance L and side a is cooled down (in a magnetic field) to a temperature below the critical temperature. The frame is kept horizontal (parallel to the x-y plane) and constarined to move in the z- direction in a non - uniform but constant magnetic field given by →B=−αx^i+(αz+B0)^k and a uniform gravitational field given by accelaration −g^k as shown in figure. The thickness of the frame is much smaller than a. Initially the frame is at rest with its centre conciding with the origin. Now the frame is released at t=0.Maximum magnitude of Z - cordinate of centre of loop during subsquent motion will be? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Super conductig square rigid frame of mass m, self inductance L and side a is cooled down (in a magnetic field) to a temperature below the critical temperature. The frame is kept horizontal (parallel to the x-y plane) and constarined to move in the z- direction in a non - uniform but constant magnetic field given by →B=−αx^i+(αz+B0)^k and a uniform gravitational field given by accelaration −g^k as shown in figure. The thickness of the frame is much smaller than a. Initially the frame is at rest with its centre conciding with the origin. Now the frame is released at t=0.Maximum magnitude of Z - cordinate of centre of loop during subsquent motion will be? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Super conductig square rigid frame of mass m, self inductance L and side a is cooled down (in a magnetic field) to a temperature below the critical temperature. The frame is kept horizontal (parallel to the x-y plane) and constarined to move in the z- direction in a non - uniform but constant magnetic field given by →B=−αx^i+(αz+B0)^k and a uniform gravitational field given by accelaration −g^k as shown in figure. The thickness of the frame is much smaller than a. Initially the frame is at rest with its centre conciding with the origin. Now the frame is released at t=0.Maximum magnitude of Z - cordinate of centre of loop during subsquent motion will be?.
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