In a region of space both electric and magnetic fields exist. A charge particle is fired in that field and it passes unaccelerated. Then

Moderate

A

$\vec{E} and \vec{B}$ are parallel
B

$\vec{E} and \vec{B}$ are mutually perpendicular
C

$\vec{E} and \vec{B}$ are mutually perpendicular and velocity of projection $\vec{V}$ must be perpendicular to both $\vec{E} and \vec{B}$ and B = EV
D

If velocity of projection is $\vec{V}$ then $\vec{E}$ , $\vec{B}$ and $\vec{V}$ must be mutually perpendicular and E = BV

Solution

Lorentz force $\vec{F} = Q \vec{V} \times \vec{B} + Q \vec{E}$
Since acceleration is zero,
$Q \vec{V} \times \vec{B} + Q \vec{E} = 0 \Rightarrow \vec{E} = \vec{B} \times \vec{V}$
From the equation it is evident that $\vec{E}$ , $\vec{B}$ and $\vec{V}$ are mutually perpendicular.

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