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Q. 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 $E =0, B \neq 0$, and initial velocity is at any angle with $B$ 1 Straight line
B $E \neq 0, B =0$ and initial velocity is at any angle with $E$ 2 Parabola
C $E \neq 0, B \neq 0, E \| B$ and initial velocity is $\perp$ to both 3 Circular
D $E \neq 0, B \neq 0, E$ perpendicular to $B$ and $v$ perpendicular to both $E$ and $B$ 4 Helical path with non-uniform pitch

Moving Charges and Magnetism

Solution:

A. Since, $E =0$ and $B \neq 0$ 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, $A \rightarrow 1,3$
B. Since, $E \neq 0$ and $B =0$.
So, path will be straight line parellel to $E$
or parabola otherwise.
Hence, $B \rightarrow 1,2$
C. $E \neq 0, B \neq 0, E \| B$
Helical path with non-uniform pitch.
Hence, $C \rightarrow 4$
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D. Straight line path if $v \times B = E$
Hence, $D \rightarrow 1$
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