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A charged particle having charge q is moving perpendicularly to the uniform magnetic field with linear speed v on a circular path of radius R. The periodic time of revolution of a particle ________.

Asked in GUJCET 2026 · Circular motion: radius, period and energy

• (1) depends on v but does not depend on R.
• (2) depends on R but does not depend on v.
• (3) do not depend on v and R both.
• (4) depend on v and R both.

Step-by-step solution

Why the other options are wrong

• (1) T=(2π R)/v does carry v, but the radius is itself R=(mv)/(qB), so the speed cancels: a faster particle simply travels a proportionally bigger circle.
• (2) The same cancellation from the other side. A larger orbit is traced at a proportionally larger speed, so the extra path length costs no extra time.
• (4) Both symbols do appear in T=(2π R)/v, but only their ratio matters, and R/v=m/(qB) is settled by the particle and the field alone.

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