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A particle of charge q is revolving in a circle of radius with a constant speed v. Find the ratio of the magnitudes of magnetic moment and angular momentum of the particle
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A particle of charge q is revolving in a circle of radius with a const...
Introduction
To find the ratio of the magnitudes of the magnetic moment (μ) and angular momentum (L) of a charged particle revolving in a circle, we start by defining these quantities.
Magnetic Moment (μ)
- The magnetic moment of a current loop is given by the formula: μ = I * A, where I is the current and A is the area.
- For a charged particle of charge q moving with speed v in a circular path of radius r:
- Current (I) = q / T, where T is the period of rotation.
- The period T can be expressed as T = 2πr / v.
- Therefore, I = qv / (2πr).
- The area (A) of the circular path is A = πr².
- Thus, the magnetic moment can be calculated as:
- μ = (qv / (2πr)) * (πr²) = (qvr / 2).
Angular Momentum (L)
- The angular momentum of a particle moving in a circle is given by: L = mvr, where m is the mass of the particle.
Ratio of Magnetic Moment to Angular Momentum
- To find the ratio μ / L:
- μ = (qvr / 2)
- L = mvr
- Therefore, the ratio becomes:
- μ / L = [(qvr / 2) / (mvr)] = (q / (2m)).
Conclusion
- The ratio of the magnitudes of magnetic moment to angular momentum for a charged particle in circular motion is:
- μ / L = q / (2m).
- This indicates that the magnetic moment is directly proportional to the charge and inversely proportional to the mass of the particle.
To find the ratio of the magnitudes of the magnetic moment (μ) and angular momentum (L) of a charged particle revolving in a circle, we start by defining these quantities.
Magnetic Moment (μ)
- The magnetic moment of a current loop is given by the formula: μ = I * A, where I is the current and A is the area.
- For a charged particle of charge q moving with speed v in a circular path of radius r:
- Current (I) = q / T, where T is the period of rotation.
- The period T can be expressed as T = 2πr / v.
- Therefore, I = qv / (2πr).
- The area (A) of the circular path is A = πr².
- Thus, the magnetic moment can be calculated as:
- μ = (qv / (2πr)) * (πr²) = (qvr / 2).
Angular Momentum (L)
- The angular momentum of a particle moving in a circle is given by: L = mvr, where m is the mass of the particle.
Ratio of Magnetic Moment to Angular Momentum
- To find the ratio μ / L:
- μ = (qvr / 2)
- L = mvr
- Therefore, the ratio becomes:
- μ / L = [(qvr / 2) / (mvr)] = (q / (2m)).
Conclusion
- The ratio of the magnitudes of magnetic moment to angular momentum for a charged particle in circular motion is:
- μ / L = q / (2m).
- This indicates that the magnetic moment is directly proportional to the charge and inversely proportional to the mass of the particle.
Community Answer
A particle of charge q is revolving in a circle of radius with a const...
q/2m
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A particle of charge q is revolving in a circle of radius with a constant speed v. Find the ratio of the magnitudes of magnetic moment and angular momentum of the particle
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A particle of charge q is revolving in a circle of radius with a constant speed v. Find the ratio of the magnitudes of magnetic moment and angular momentum of the particle for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A particle of charge q is revolving in a circle of radius with a constant speed v. Find the ratio of the magnitudes of magnetic moment and angular momentum of the particle covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle of charge q is revolving in a circle of radius with a constant speed v. Find the ratio of the magnitudes of magnetic moment and angular momentum of the particle.
A particle of charge q is revolving in a circle of radius with a constant speed v. Find the ratio of the magnitudes of magnetic moment and angular momentum of the particle for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A particle of charge q is revolving in a circle of radius with a constant speed v. Find the ratio of the magnitudes of magnetic moment and angular momentum of the particle covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle of charge q is revolving in a circle of radius with a constant speed v. Find the ratio of the magnitudes of magnetic moment and angular momentum of the particle.
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