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.

Options

A. (i), (ii)
B. (i), (iv)
C. (ii), (iii)
D. (iii), (iv)

Answer

D

Explanation

if `theta =0^(@)`, due to magnetic force, particle moves in a circle but due to electric force `qE_(0)`, its speed is increasing along `+y`-axis. The path will be helical with increasing pitch.
(i), (ii) are incorrect, (iii) is correct.
(iv) if `theta = 90^(@), F_(m) = 0`, the particle moves in a straight line with increasing speed along y-axis