Consider the motion of a positive point charge in a region where there are simultaneous uniform eletric and magnetic field `E=E_0hatj` and `B=B_0hatj`. At time `t=0`, this charge has velocity 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 `tgt0?`
a. If `theta=0^0` the charge moves in a circular path in the xy-plane.
`b.If theta=0^0` the charge undergoes helical motion with constant pitch along the y-axis.
c. If `theta=1 0^0` the charge undergoes helicalmotion 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.

Options

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

(c,d)

Explanation

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)