Q24. Under the influence of a uniform magnetic field, a charged particle moves with a constant speed

Q: What is the correct answer for CUET UG Physics Q24?

The correct answer is b. When a charged particle of mass 'm' and charge 'q' moves with velocity 'v' perpendicular to a uniform magnetic field 'B', the magnetic Lorentz force (F_m = qvB) provides the necessary centripetal force (F_c = mv²/r). Equating these forces: qvB = mv²/r. From this, the radius of the circular path is r = mv/(qB). The time period of revolution (T) is the time taken to complete one full circle, given b

Q: Q24. Under the influence of a uniform magnetic field, a charged particle moves with a constant speed v in a circle of radius r. The time period of the revolution of the particle: (a) depends on v and…

The correct answer is b. When a charged particle of mass 'm' and charge 'q' moves with velocity 'v' perpendicular to a uniform magnetic field 'B', the magnetic Lorentz force (F_m = qvB) provides the necessary centripetal force (F_c = mv²/r). Equating these forces: qvB = mv²/r. From this, the radius of the circular path is r = mv/(qB). The time period of revolution (T) is the time taken to complete one full circle, given b

Q: What are the options for this CUET UG Physics question?

A. depends on v and not on r · B. is independent of both v and r · C. depends on r and not on v · D. depends on both v and r

Question

Q24. Under the influence of a uniform magnetic field, a charged particle moves with a constant speed v in a circle of radius r. The time period of the revolution of the particle:
(a) depends on v and not on r
(b) is independent of both v and r
(c) depends on r and not on v
(d) depends on both v and r

FirstInTest · Accepted Answer

When a charged particle of mass 'm' and charge 'q' moves with velocity 'v' perpendicular to a uniform magnetic field 'B', the magnetic Lorentz force (F_m = qvB) provides the necessary centripetal force (F_c = mv²/r). Equating these forces: qvB = mv²/r. From this, the radius of the circular path is r = mv/(qB). The time period of revolution (T) is the time taken to complete one full circle, given by T = (circumference) / (speed) = (2πr) / v. Substituting the expression for r: T = (2π/v) * (mv/(qB)) = 2πm/(qB). This formula for the time period shows that T depends only on the mass (m) and charge (q) of the particle, and the strength of the magnetic field (B). It is independent of both the particle's speed (v) and the radius (r) of its circular path. Therefore, option (b) is the correct statement. Options (a), (c), and (d) are incorrect as they suggest dependence on v or r.

Answer

depends on v and not on r

Answer

is independent of both v and r

Answer

depends on r and not on v

Answer

depends on both v and r

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