Question

A charged particle with some initial velocity is projected in a region where non-zero electric and/or magnetic fields are present. In Column I, information about the existence of electric and/or magnetic field and direction of initial velocity of charged particle are given, while in Column II the probable path of the charged particle is mentioned. Match the entries of Column I with the entries of Column II.

Column I		Column II
A	$E=0,B\ne 0$, and initial velocity is at any angle with $B$	1	Straight line
B	$E\ne 0,B=0$ and initial velocity is at any angle with $E$	2	Parabola
C	$E\ne 0,B\ne 0,E\Vert B$ and initial velocity is $\perp$ to both	3	Circular
D	$E\ne 0,B\ne 0,E$ perpendicular to $B$ and $v$ perpendicular to both $E$ and $B$	4	Helical path with non-uniform pitch

• A. A - (1,3) , B - (1,2) , C - (4) , D - (1)
• B. A - (1,2) , B - (3,4) , C - (4) , D - (1,3)
• C. A - (2) , B - (3) , C - (1) , D - (4)
• D. A - (4) , B - (1) , C - (2) , D - (3)

Answer 1

Answer: (A)

A. Since, $E=0$ and $B\ne 0$ so path will be straight line.
If velocity is parallel to $B$,
or path will be circular if $v\perp B$,
or path will be helical (with uniform pitch) if $v$ is at same other angle to $B$.
Hence, $A\to 1,3$
B. Since, $E\ne 0$ and $B=0$.
So, path will be straight line parellel to $E$
or parabola otherwise.
Hence, $B\to 1,2$
C. $E\ne 0,B\ne 0,E\Vert B$
Helical path with non-uniform pitch.
Hence, $C\to 4$

D. Straight line path if $v\times B=E$
Hence, $D\to 1$