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A charged particle with charge q enters a region of constant, uniform, and mutually orthogonal fields E and B with a velocity v perpendicular to both E and B and comes out without any change in magnitude or direction of v. Then

1. v = B × E / E²
2. v = E × B / B²
3. v = B × E / B²
4. v = E × B / E²

Correct answer: v = E × B / B²

Solution

The correct option is derived from the condition that the net force acting on the charged particle must be zero for it to maintain its velocity. In a uniform electric field E and magnetic field B, the electric force qE and the magnetic force q(v × B) must balance each other, leading to the relationship v = E × B / B².

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