Question

A charged particle with some initial velocity is projected in a region where non-zero uniform electric and/or magnetic fields are present. In column I, information about the existence of a electric and/or magnetic field and direction of initial velocity of charged is mentioned. Match the entries of Column I with the entries of Column II (Consider all possibilities)

$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ \text{(a)}& \overrightarrow{E}=0,\overrightarrow{B}\ne 0\text{and initial velocity may be at any angle with}\overrightarrow{B}\text{including}{0}^{\circ }& \text{(p)}& \text{Straight line}\\ \text{(b)}& \overrightarrow{E}\ne 0,\overrightarrow{B}=0\text{and initial velocity may be at any angle with}\overrightarrow{E}\text{including}{0}^{\circ }& \text{(q)}& \text{Parabola}\\ \text{(c)}& \overrightarrow{E}\ne 0,\overrightarrow{B}\ne 0\overrightarrow{E}||\overrightarrow{B}\text{and initial velocity is}\perp \text{to both}\overrightarrow{E}\text{and}\overrightarrow{B}& \text{(r)}& \text{Circular}\\ \text{(d)}& \overrightarrow{E}\ne 0,\overrightarrow{B}\ne 0,\overrightarrow{E}\text{is perpendicular to B and initial velocity is perpendicular to both}\overrightarrow{E}\text{and}\overrightarrow{B}& \text{(s)}& \text{Helical path}\end{array}$

• A. a – prs, b – pq, c – s, d – p
• B. a – qrs, b – pqr, c – s, d – rs
• C. a – qr, b – pqrs, c – pq, d – qs
• D. a – prs, b – pq, c – ps, d – pr

Answer 1

The correct option is A

a – prs, b – pq, c – s, d – p

(a) Since $\overrightarrow{E}=0$ and $\overrightarrow{B}\ne 0$, so path will be straight line if velocity is parallel to $\overrightarrow{B}$. Or path will be circular if $\overrightarrow{V}\perp \overrightarrow{B}$. Or path will be helical (with uniform pitch) if $\overrightarrow{V}$ is at some other angle to $\overrightarrow{B}$. Hence $\left(a\right)\to p,r,s$

(b) Since $\overrightarrow{E}\ne 0$ and $\overrightarrow{B}=0$, so path will be straight line if $\overrightarrow{v}||\overrightarrow{B}$ or parabola otherwise. Hence $\left(b\right)\to )p,q$

(c) $\overrightarrow{E}\ne 0,\overrightarrow{B}\ne 0,\overrightarrow{E}||\overrightarrow{B}$
Helical path with non-uniform pitch Hence $\left(c\right)\to s$

(d) Straight line if $\overrightarrow{V}\times \overrightarrow{B}=\overrightarrow{E}$ Hence $\left(d\right)\to p$