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A charged particle is moving in a cyclotron, what effect on the radius of path of this charged particle will occur when the frequency of the radio frequency field is doubled?
- a)It will also be doubled.
- b)It will be halved.
- c)It will be increased by four times.
- d)It will remain unchanged.
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A charged particle is moving in a cyclotron, what effect on the radius...
As frequency of revolution in a cyclotron
vC = Bq/2πm is independent of r.
So the radius of path in the dees will remain unchanged. When the frequency is changed.
vC = Bq/2πm is independent of r.
So the radius of path in the dees will remain unchanged. When the frequency is changed.
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A charged particle is moving in a cyclotron, what effect on the radius...
Effect of changing the frequency of the radio frequency field on the radius of path of a charged particle in a cyclotron.
Introduction
A cyclotron is a type of particle accelerator that uses a high-frequency alternating voltage to accelerate charged particles. It consists of two D-shaped hollow metal electrodes called dees, which are placed facing each other and connected to a high-frequency alternating voltage source. A magnetic field perpendicular to the plane of the dees is also applied.
Working of a Cyclotron
1. The charged particle, initially at the center of the cyclotron, is accelerated by the electric field in the gap between the dees.
2. As the particle gains energy, it moves in a spiral path due to the perpendicular magnetic field.
3. The frequency of the alternating voltage applied to the dees is adjusted to match the time taken by the particle to complete one revolution in the cyclotron. This ensures that the particle receives a continuous acceleration.
Effect of Changing Frequency on the Radius of Path
When the frequency of the radio frequency field is doubled, it does not have a direct effect on the radius of the path of the charged particle. This is because the radius of the path is determined by the combination of the initial velocity of the particle, the strength of the magnetic field, and the mass-to-charge ratio of the particle.
Centripetal Force and Magnetic Force
The centripetal force acting on the charged particle is provided by the magnetic force. The magnetic force is given by the equation:
F = qvB
where F is the force, q is the charge of the particle, v is its velocity, and B is the strength of the magnetic field.
Centripetal Force and Radius of Path
The centripetal force required for the particle to move in a circular path is given by the equation:
F = m(v^2/r)
where m is the mass of the particle and r is the radius of the path.
Equating Centripetal Force and Magnetic Force
By equating the centripetal force and the magnetic force, we can derive an expression for the radius of the path:
qvB = m(v^2/r)
Simplifying this equation, we get:
r = mv/(qB)
Conclusion
From the derived equation, it can be seen that the radius of the path is not dependent on the frequency of the radio frequency field. Therefore, when the frequency is doubled, the radius of the path remains unchanged. The correct answer is option 'D'.
Introduction
A cyclotron is a type of particle accelerator that uses a high-frequency alternating voltage to accelerate charged particles. It consists of two D-shaped hollow metal electrodes called dees, which are placed facing each other and connected to a high-frequency alternating voltage source. A magnetic field perpendicular to the plane of the dees is also applied.
Working of a Cyclotron
1. The charged particle, initially at the center of the cyclotron, is accelerated by the electric field in the gap between the dees.
2. As the particle gains energy, it moves in a spiral path due to the perpendicular magnetic field.
3. The frequency of the alternating voltage applied to the dees is adjusted to match the time taken by the particle to complete one revolution in the cyclotron. This ensures that the particle receives a continuous acceleration.
Effect of Changing Frequency on the Radius of Path
When the frequency of the radio frequency field is doubled, it does not have a direct effect on the radius of the path of the charged particle. This is because the radius of the path is determined by the combination of the initial velocity of the particle, the strength of the magnetic field, and the mass-to-charge ratio of the particle.
Centripetal Force and Magnetic Force
The centripetal force acting on the charged particle is provided by the magnetic force. The magnetic force is given by the equation:
F = qvB
where F is the force, q is the charge of the particle, v is its velocity, and B is the strength of the magnetic field.
Centripetal Force and Radius of Path
The centripetal force required for the particle to move in a circular path is given by the equation:
F = m(v^2/r)
where m is the mass of the particle and r is the radius of the path.
Equating Centripetal Force and Magnetic Force
By equating the centripetal force and the magnetic force, we can derive an expression for the radius of the path:
qvB = m(v^2/r)
Simplifying this equation, we get:
r = mv/(qB)
Conclusion
From the derived equation, it can be seen that the radius of the path is not dependent on the frequency of the radio frequency field. Therefore, when the frequency is doubled, the radius of the path remains unchanged. The correct answer is option 'D'.
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A charged particle is moving in a cyclotron, what effect on the radius of path of this charged particle will occur when the frequency of the radio frequency field is doubled?a)It will also be doubled.b)It will be halved.c)It will be increased by four times.d)It will remain unchanged.Correct answer is option 'D'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A charged particle is moving in a cyclotron, what effect on the radius of path of this charged particle will occur when the frequency of the radio frequency field is doubled?a)It will also be doubled.b)It will be halved.c)It will be increased by four times.d)It will remain unchanged.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A charged particle is moving in a cyclotron, what effect on the radius of path of this charged particle will occur when the frequency of the radio frequency field is doubled?a)It will also be doubled.b)It will be halved.c)It will be increased by four times.d)It will remain unchanged.Correct answer is option 'D'. Can you explain this answer?.
A charged particle is moving in a cyclotron, what effect on the radius of path of this charged particle will occur when the frequency of the radio frequency field is doubled?a)It will also be doubled.b)It will be halved.c)It will be increased by four times.d)It will remain unchanged.Correct answer is option 'D'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A charged particle is moving in a cyclotron, what effect on the radius of path of this charged particle will occur when the frequency of the radio frequency field is doubled?a)It will also be doubled.b)It will be halved.c)It will be increased by four times.d)It will remain unchanged.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A charged particle is moving in a cyclotron, what effect on the radius of path of this charged particle will occur when the frequency of the radio frequency field is doubled?a)It will also be doubled.b)It will be halved.c)It will be increased by four times.d)It will remain unchanged.Correct answer is option 'D'. Can you explain this answer?.
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