Question

Consider the motion of a positive point charge in a region where area simultaneous uniform electric and magnetic fields ` vec(E) = E_(0) hat(j)` and ` vec(B) = B_(0) hat(j)`. At time ` t = 0` , this charge has velocity ` vec(v)` in the ` x-y `plane , making an angle ` theta` with the ` x-axis `. Which of the following option(s) is (are) correct for time ` t gt 0`?
A. If `theta=0^@`, the charge moves in a circular path in the x-z plane
B. If `theta=0^@`, the charge undergoes helical motion with constant pitch along the y-axis
C. If `theta=10^@`, the charge undergoes helical motion with its pitch increasing with time, along the y-axis
D. If `theta=90^@`, the charge undergoes linear but accelerated motion along the y-axis

Answer 1

Correct Answer - (c,d)
If `theta=0^@` then due to magnetic force path is circular but due
to force `qE_0(uarr)q` will have accelerated motion along y-axis. So
combined path of q will be a helical
path with variable pitch so (a) and
(b) are wrong.
If `theta=10^@`, then dut to `v cos theta`, path
is circular and due to `qE_0` and v sin
`theta`, q has accelerated motion along
y-axis so combined path is a helical
path with variable pitch (C) is correct.
If `theta=90^@ then F_B=0` and due to `qE_0` motion is accelerated along
y-axis. (d)