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`?

Options

A. If `theta=0^(@)`, the charge moves in a circular path in the `x-y` 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 veriable pitch so `(A)` and `(B)` are wrong.If `theta=10^(@)` then due to `vcostheta`,path is circular and due to `qE_(0)` and `vsintheta`,`q` has accelerated motion along `y`-axis so combined path is 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)`