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A 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 in terms of m, g, L , a and alpha?
Maximum magnitude of Z - cordinate of centre of loop during subsquent motion will be in terms of m, g, L , a and alpha?
Most Upvoted Answer
A super conductig square rigid frame of mass m, self inductance L and ...
Understanding the System
The superconducting square frame is subject to both gravitational and magnetic forces. The frame's motion is influenced by the Lorentz force due to the non-uniform magnetic field and its self-inductance.
Magnetic Field Analysis
- The magnetic field is given as:
\(\vec{B} = -\alpha x \hat{i} + (\alpha z + B_0) \hat{k}\)
- This implies that the magnetic field varies with the x-coordinate and has a z-component that depends on the height of the frame.
Forces Acting on the Frame
- **Gravitational Force**: The gravitational force acting on the frame is \(F_g = mg\) directed downward (\(-\hat{k}\)).
- **Lorentz Force**: The motion of the superconducting frame generates an induced current due to the change in magnetic flux. The induced electromotive force (emf) is given by Faraday's Law, and the resulting Lorentz force can be expressed as:
\(F_L = I \cdot (\vec{L} \times \vec{B})\).
Maximal Z-Coordinate Calculation
Upon release, the frame experiences a net force influenced by gravity and the Lorentz force. The motion can be analyzed using energy conservation principles:
- The maximum height reached can be derived from the balance of forces and energy conservation:
\[
\frac{1}{2} m v^2 = mgh + \text{Magnetic Potential Energy}
\]
- The maximum height \(Z_{max}\) can be expressed in terms of parameters \(m\), \(g\), \(L\), \(a\), and \(\alpha\).
Final Expression
The final expression for the maximum magnitude of the Z-coordinate of the frame, considering the gravitational and magnetic influences, can be simplified to:
\[
Z_{max} = \frac{L \alpha a^2}{mg} + \text{constant}
\]
This encapsulates the interplay between gravitational and magnetic effects as the frame moves through the magnetic field, resulting in a maximum height that depends on the system's parameters.
The superconducting square frame is subject to both gravitational and magnetic forces. The frame's motion is influenced by the Lorentz force due to the non-uniform magnetic field and its self-inductance.
Magnetic Field Analysis
- The magnetic field is given as:
\(\vec{B} = -\alpha x \hat{i} + (\alpha z + B_0) \hat{k}\)
- This implies that the magnetic field varies with the x-coordinate and has a z-component that depends on the height of the frame.
Forces Acting on the Frame
- **Gravitational Force**: The gravitational force acting on the frame is \(F_g = mg\) directed downward (\(-\hat{k}\)).
- **Lorentz Force**: The motion of the superconducting frame generates an induced current due to the change in magnetic flux. The induced electromotive force (emf) is given by Faraday's Law, and the resulting Lorentz force can be expressed as:
\(F_L = I \cdot (\vec{L} \times \vec{B})\).
Maximal Z-Coordinate Calculation
Upon release, the frame experiences a net force influenced by gravity and the Lorentz force. The motion can be analyzed using energy conservation principles:
- The maximum height reached can be derived from the balance of forces and energy conservation:
\[
\frac{1}{2} m v^2 = mgh + \text{Magnetic Potential Energy}
\]
- The maximum height \(Z_{max}\) can be expressed in terms of parameters \(m\), \(g\), \(L\), \(a\), and \(\alpha\).
Final Expression
The final expression for the maximum magnitude of the Z-coordinate of the frame, considering the gravitational and magnetic influences, can be simplified to:
\[
Z_{max} = \frac{L \alpha a^2}{mg} + \text{constant}
\]
This encapsulates the interplay between gravitational and magnetic effects as the frame moves through the magnetic field, resulting in a maximum height that depends on the system's parameters.
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A 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 in terms of m, g, L , a and alpha?
Question Description
A 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 in terms of m, g, L , a and alpha? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A 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 in terms of m, g, L , a and alpha? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 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 in terms of m, g, L , a and alpha?.
A 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 in terms of m, g, L , a and alpha? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A 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 in terms of m, g, L , a and alpha? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 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 in terms of m, g, L , a and alpha?.
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A 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 in terms of m, g, L , a and alpha?, a detailed solution for A 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 in terms of m, g, L , a and alpha? has been provided alongside types of A 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 in terms of m, g, L , a and alpha? theory, EduRev gives you an
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