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Under the influence of a uniform magnetic field,a charged particle moves with constant speed vin a circle of radius R. The time period of rotationof the particle: [2009]
- a)depends on R and not on v
- b)is independent of both v and R
- c)depends on both v and R
- d)depends on v and not on R
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Under the influence of a uniform magnetic field,a charged particle mov...
The time period of the charged particle is
given by
given by
Thus, time period is independent of both v and R.
Most Upvoted Answer
Under the influence of a uniform magnetic field,a charged particle mov...
Understanding the Motion of Charged Particles in a Magnetic Field
When a charged particle moves in a uniform magnetic field, it experiences a force known as the Lorentz force, which acts perpendicular to its velocity. This force causes the particle to move in a circular path.
Key Factors in Circular Motion
- Centripetal Force: The magnetic force acts as the centripetal force, keeping the particle in circular motion.
- Magnetic Force Formula: The magnetic force acting on a charged particle is given by F = qvB, where:
- q is the charge of the particle,
- v is the speed of the particle,
- B is the magnetic field strength.
- Centripetal Force Requirement: For circular motion, the required centripetal force is given by F = mv²/R, where:
- m is the mass of the particle,
- R is the radius of the circular path.
Deriving the Time Period
When equating the magnetic force to the centripetal force:
- qvB = mv²/R
From this, we can derive the relationship for the radius R:
- R = mv/(qB)
Now, the time period T of one complete rotation is given by:
- T = Circumference / Speed = (2πR) / v
Substituting R from the earlier relationship:
- T = (2π(mv/(qB))) / v = (2πm)/(qB)
Conclusion: Independence of T
- Dependence: The time period T depends solely on the mass of the particle (m), charge (q), and magnetic field strength (B).
- Independence from v and R: This shows that T is independent of both the speed (v) and the radius (R) of the circular path.
Thus, the correct answer is indeed option B: the time period of rotation is independent of both v and R.
When a charged particle moves in a uniform magnetic field, it experiences a force known as the Lorentz force, which acts perpendicular to its velocity. This force causes the particle to move in a circular path.
Key Factors in Circular Motion
- Centripetal Force: The magnetic force acts as the centripetal force, keeping the particle in circular motion.
- Magnetic Force Formula: The magnetic force acting on a charged particle is given by F = qvB, where:
- q is the charge of the particle,
- v is the speed of the particle,
- B is the magnetic field strength.
- Centripetal Force Requirement: For circular motion, the required centripetal force is given by F = mv²/R, where:
- m is the mass of the particle,
- R is the radius of the circular path.
Deriving the Time Period
When equating the magnetic force to the centripetal force:
- qvB = mv²/R
From this, we can derive the relationship for the radius R:
- R = mv/(qB)
Now, the time period T of one complete rotation is given by:
- T = Circumference / Speed = (2πR) / v
Substituting R from the earlier relationship:
- T = (2π(mv/(qB))) / v = (2πm)/(qB)
Conclusion: Independence of T
- Dependence: The time period T depends solely on the mass of the particle (m), charge (q), and magnetic field strength (B).
- Independence from v and R: This shows that T is independent of both the speed (v) and the radius (R) of the circular path.
Thus, the correct answer is indeed option B: the time period of rotation is independent of both v and R.
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Under the influence of a uniform magnetic field,a charged particle moves with constant speed vin a circle of radius R. The time period of rotationof the particle: [2009]a)depends on R and not on vb)is independent of both v and Rc)depends on both v and Rd)depends on v and not on RCorrect answer is option 'B'. Can you explain this answer? for Class 12 2026 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Under the influence of a uniform magnetic field,a charged particle moves with constant speed vin a circle of radius R. The time period of rotationof the particle: [2009]a)depends on R and not on vb)is independent of both v and Rc)depends on both v and Rd)depends on v and not on RCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 12 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Under the influence of a uniform magnetic field,a charged particle moves with constant speed vin a circle of radius R. The time period of rotationof the particle: [2009]a)depends on R and not on vb)is independent of both v and Rc)depends on both v and Rd)depends on v and not on RCorrect answer is option 'B'. Can you explain this answer?.
Under the influence of a uniform magnetic field,a charged particle moves with constant speed vin a circle of radius R. The time period of rotationof the particle: [2009]a)depends on R and not on vb)is independent of both v and Rc)depends on both v and Rd)depends on v and not on RCorrect answer is option 'B'. Can you explain this answer? for Class 12 2026 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Under the influence of a uniform magnetic field,a charged particle moves with constant speed vin a circle of radius R. The time period of rotationof the particle: [2009]a)depends on R and not on vb)is independent of both v and Rc)depends on both v and Rd)depends on v and not on RCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 12 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Under the influence of a uniform magnetic field,a charged particle moves with constant speed vin a circle of radius R. The time period of rotationof the particle: [2009]a)depends on R and not on vb)is independent of both v and Rc)depends on both v and Rd)depends on v and not on RCorrect answer is option 'B'. Can you explain this answer?.
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