Magnetics 1 Question 19

19. Consider the motion of a positive point charge in a region where there are simultaneous uniform electric and magnetic fields E=E0j^ and B=B0j^. At time t=0, this charge has velocity v in the xy plane, making an angle θ with the x-axis. Which of the following option(s) is(are) correct for time t>0 ?

(2012)

(a) If θ=0, the charge moves in a circular path in the xz 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.

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Answer:

Correct Answer: 19. (c, d)

Solution:

  1. and Magnetic field will rotate the particle in a circular path (in xz plane or perpendicular to B ). Electric field will exert a constant force on the particle in positive y-direction. Therefore, resultant path is neither purely circular nor helical or the options (a) and (b) both are wrong.

v and B will rotate the particle in a circular path in xz plane (or perpendicular to B ). Further v|and E will move the particle (with increasing speed) along positive y-axis (or along the axis of above circular path). Therefore, the resultant path is helical with increasing pitch, along the y-axis (or along B and E ). Therefore option (c) is correct.

(d)

Magnetic force is zero, as θ between B and v is zero. But electric force will act in y-direction. Therefore, motion is 1D and uniformly accelerated (towards positive y-direction).



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