Consider the motion of a positive point charge in a region where there are simultaneous uniform electic and magnetic field `E=E_0hatj` and `B=B_0hatj`. At time `t=0`, this charge has velocity v inn the xy-plane making an angle `theta` with the x-axis. Which of the following option(s) is (are) correct for time `tgt0?`
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=10^0` 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.

Explanation

Magnetic field will rotate the particle in as circulr path (in-`xz`-plane or perpendicular to `B`). Electric field exert a constant force to the particle in positive `y`-direction. Therefore, resultannt path is neither purely circular nor helical or the options a and b both are wrong.
c. `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 wilth increasing pitch along the y-axis (or along `B` and `E`). Therefore option c is correct.

Magnetic force is zero, as `theta` between `B` and `v` is zero. But electric force will act in y-direction. Therefore, moto is `1-D` and uniformly accelerated (towards positive y-direction). Therefore, option d is also correct.