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JEE MainPhysicsMagnetic Effects of Current

A region contains parallel uniform electric and magnetic fields directed along the positive z-axis, given by E = E₀ k and B = B₀ k . A charged particle of mass m and charge q is projected from the origin with an initial velocity v = v₀ i . What is the speed of the particle after a time t ?

Options

  1. Av₀ + q E₀ t m
  2. Bq E₀ t m
  3. Cv₀^2 + ( q E₀ t m )^2
  4. Dv₀^2 + ( q B₀ t m )^2

Correct answer

C. v₀^2 + ( q E₀ t m )^2

Step-by-step solution

The particle experiences forces from both the electric and magnetic fields. The magnetic force F _m = q( v B ) acts in the x-y plane because B is along the z-axis. Since magnetic force does no work, it only changes the direction of the velocity component perpendicular to B , keeping its magnitude constant. Thus, the speed in the x-y plane remains v_ xy = v₀ . The electric force F _e = q E = q E₀ k provides a constant acceleration along the z-axis: a_z = q E₀ m . The initial velocity in the z-direction is zero. Afte

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