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Question:

Consider the motion of a positive point charge in a region where there are simultaneous uniform electric and magnetic fields →E=E0^j and →B=B0^j. 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 time t > 0?

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

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

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

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

Solution:

If θ=90°, Bexerts no force on q as sin90°=0. If θ=10°, the charge particle moves in a helix due to the electric force along the Y-axis. The electric field causes acceleration along the y-axis, resulting in an increasing pitch of the helix over time. If θ=0°, the charge will move in a circle in the x-z plane due to the magnetic field, but it will also have a constant velocity in the y direction due to the electric field. This results in helical motion with constant pitch along the y-axis. Therefore, options 1, 3, and 4 are correct.