Lorentz force – An IIT-JEE 2012 Multiple Correct Answer(s) Type Question

“Making the simple complicated is commonplace; making the complicated simple, awesomely simple, that’s creativity.”

– Charles Mingus    

IIT-JEE Multiple Correct Answer(s) Type Questions are designed to have four choices (A), (B), (C) and (D) out of which ONE or MORE are correct. The following question appeared in IIT-JEE 2012 question paper. The question is meant for checking your understanding of Lorentz forces.

Consider the motion of a positive point charge in a region where there are simultaneous uniform electric and magnetic fields E = E₀ ĵ and B = B₀ ĵ. At time t = 0, this charge has velocity v in the x-y plane, making an angle θ with the x-axis. Which of the following option(s) is (are) correct for t > 0?

(A) If θ = 0°, the charge moves in a circular path in the x-z plane.

(B) If θ = 0°, the charge undergoes helical motion with constant pitch along the y-axis.

(C) If θ = 10°, the charge undergoes helical motion with its pitch increasing with time, along the y-axis.

(D) If θ = 90°, the charge undergoes linear but accelerated motion along the y-axis.

Note that the electric and magnetic fields are along the positive y-direction.

If θ = 0, the charged particle is moving at right angles to the electric and magnetic fields (Fig.). The magnetic force (qv×B₀) will make the particle move along a circle and the electric force (qE₀) will push it along the positive y-direction. The path of the particle will therefore be a helix of increasing pitch.

If θ = 10°,the magnetic field will make the particle move along the positive y-direction, following a helical path of constant pitch; but since the electric force (qE₀) pushes it along the positive y-direction, the helical path has increasing pitch.

If θ = 90°, the charged particle is moving parallel to the electric and magnetic fields. The magnetic field has no action on the motion since there is no magnetic force. But the electric force (qE₀) will push the particle along the positive y-direction. The particle is thus in accelerated linear motion. 

Therefore options (C) and (D) are correct.