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A particle with charge -q and mass m revolves in a circular path of radius r around an infinitely long charged wire with linear charge density +λ. What is the time period of its motion?
- T = 2π√(m/2kλq)
- T = √(4π²m³/2kλq)
- T = 2π√(m/kλq)
- T = √(m/2kλq)
Correct answer: T = 2π√(m/2kλq)
Solution
The charged particle experiences a centripetal force due to the electric field created by the charged wire. Equating the centripetal force to the electrostatic force and solving for the time period, we find that it depends on the mass, charge, and the linear charge density of the wire, leading to the given expression.
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