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A charged particle is projected with velocity $\vec{V}$ in a region of space where both electric field $\vec{E}$ and magnetic field $\vec{B}$ exist. Then the particle will pass through that region with constant velocity if.

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$\vec{E}, \vec{B} and \vec{V}$ are mutually perpendicular.

$\vec{E}, \vec{B} and \vec{V}$ are parallel each other.

$\vec{E} and \vec{B}$ are mutually perpendicular and $V = E / B .$

$\vec{E}, \vec{B} and \vec{V}$ are mutually perpendicular and $V = E / B .$

answer is D.

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Detailed Solution

$\vec{E}, \vec{B} and \vec{V}$ are mutually perpendicular and lorentz force must be zero i.e.
$Q \vec{E} + Q \vec{V} \times \vec{B} = 0 \Rightarrow V = E / B .$

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