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In a certain region of space electric field \( \vec{E} \) and magnetic field \( \vec{B} \) are perpendicular to each other and an electron enters in region perpendicular to the direction of \( \vec{B} \) and \( \vec{E} \) both and moves undeflected, then velocity of electron is
- \( \vec{E} \)
- \( \vec{E} \times \vec{B} \)
- \( \vec{B} \)
- \( \frac{\vec{E}}{\vec{B}} \)
Correct answer: \( \frac{\vec{E}}{\vec{B}} \)
Solution
For the electron to move undeflected, the electric force and magnetic force must cancel each other. This condition is satisfied when the velocity of the electron is given by \( \vec{v} = \frac{\vec{E}}{\vec{B}} \), as the magnitudes of the forces become equal and opposite.
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