Consider the motion of a positive point charge in a region where are simultaneous uniform electric and magnetic field $E = E_{0} \hat{j}$ and $B = B_{0} \hat{j}$ . At time $t = 0$ , this charge has velocity $v$ in the x-y plane, making an angle $θ$ with the x-axis. Which of the following option(s) is (are) correct for time $t > 0$ ?

Question

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Answer 1

If $θ = 0^{o}$ then due to magnetic force path is circular but due to force $q E_{0} (↑) q$ will have accelerated motion along y-axis. So combined path of q will be a helical path with variable pitch so (a) and (b) are wrong.
If $θ = 1 0^{o}$ , then due to $v c o s θ$ , path is circular and due to $q E_{0}$ and $v s i n θ$ , q has accelerated motion along y-axis so combined path is a helical path with variable pitch (C) is correct.
If $θ = 9 0^{o}$ then $F_{B} = 0$ and due to $q E_{0}$ motion is accelerated along y-axis (D).

Answer 2

If

θ = 0^{o}

then due to magnetic force path is circular but due to force

q E_{0} (↑) q

will have accelerated motion along y-axis. So combined path of q will be a helical path with variable pitch so (a) and (b) are wrong.
If

θ = 1 0^{o}

, then due to

v c o s θ

, path is circular and due to

q E_{0}

and

v s i n θ

, q has accelerated motion along y-axis so combined path is a helical path with variable pitch (C) is correct.
If

θ = 9 0^{o}

then

F_{B} = 0

and due to

q E_{0}

motion is accelerated along y-axis (D).