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

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Solution

Case A:
$\to E = 0$
$\Rightarrow_{E} = 0$
If initial velocity $\to v$ is at an angle to $\to B$ , there will be a component along $\to B$ and a component $⊥ \to B$
The $⊥$ component is responsible for circular motion in the plane $⊥$ to $\to B$ .
The parallel component to $\to B$ is responsible for motion along $\to B$ .
If $\to v ∥ \to B$ , the motion will be along $\to B$ only.
Case B:
If $\to v ∥ t o \to E$ , there will be acceleration if charge is positive, deceleration if the charge is negative.
If $\to v ∦ t o \to E$ , the trajectory will be a parabola.
Case C:
$\to E \neq 0$
$\to B \neq 0$
$\to E ∥ \to B$
Path will be helical since component $∥ \to B$ and $v e c E$ will move the particle along this direction.
Component $⊥ \to B$ will make the particle move in a circle.
Hence, the combined motion will be helical.
Case D:
$\to E \neq 0$
$\to B \neq 0$
$\to v ⊥ \to E$
$\to v ⊥ \to B$
$_{m a g} ∥ \to E$ or $_{m a g} ∥ (- \to E)$
Hence, path will be a parabola in general.
If $_{m a g} ∥ (- \to E)$ and both magnitudes are equal, the path will be a straight line.
Hence,
$A \to 1, 3$
$B \to 1, 2$
$C \to 4$
$D \to 1, 2$

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