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JEE Main20207 Jan 2020Evening ShiftPhysicsElectrostaticsActual

A particle of mass m and charge q has an initial velocity v → = v 0 j ^ . If an electric field E → = E 0 i ^ and magnetic field B → = B 0 i ^ act on the particle, its speed will double after a time

Options

  1. A2 m v 0 q E 0
  2. B3 m v 0 q E 0
  3. C3 m v 0 qE 0
  4. D2 m v 0 qE 0

Correct answer

C. 3 m v 0 qE 0

Step-by-step solution

Acceleration produced by electric field, a = q E 0 m i ^ After time t , velocity of the particle, v = u + a t ⇒ v = v 0 j ^ + q E 0 t m i ^   ∵ u = v = v 0 j ^ So, speed of the particle, v = v 0 2 + q E 0 t m 2 Now, given v = 2 v 0 after time t , so 2 v 0 = v 0 2 + q E 0 t m 2 ⇒   4 v 0 2 = v 0 2 + q E 0 t m 2 ⇒   3 v 0 2 = q E 0 t m 2 So, time interval, t = 3 m v 0 q E 0 Here, we must note that no change in magnitude of velocity is caused by a perpendicular magnetic field. So

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