Problem

Consider the motion of a positive point charge in a region where there are simultaneous uniform electric and magnetic fields

\mathbf{E} = E_0 \hat{\mathbf{j}}

and

\mathbf{B} = B_0 \hat{\mathbf{j}}

. At time

t = 0

, this charge has velocity

\mathbf{v}

in the

xy

-plane making an angle

\theta

with the

x

-axis. Which of the following option(s) is(are) correct for time

t > 0

? (JEE 2012) a. - (a) If

\theta = 0^\circ

, the charge moves in a circular path in the

xz

-plane. b. - (b) If

\theta = 0^\circ

, the charge undergoes helical motion with constant pitch along the

y

-axis c. - (c) If

\theta = 10^\circ

, the charge undergoes helical motion with its pitch increasing with time along the

y

-axis. d. - (d) If

\theta = 90^\circ

, the charge undergoes linear but accelerated motion along the

y

-axis.