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-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)`