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A particle having a mass of 10⁻² kg carries a charge of 5 × 10⁻⁸C. The particle is given an initial horizontal velocity of 10⁵ ms⁻¹ in the presence of electric field E̅ and magnetic field B̅. To keep the particle moving in a horizontal direction, it is necessary that:

1. B̅ should be perpendicular to the direction of velocity and E̅ should be along the direction of velocity.
2. Both B̅ and E̅ should be along the direction of velocity.
3. Both B̅ and E̅ are mutually perpendicular and perpendicular to the direction of velocity.
4. B̅ should be along the direction of velocity and E̅ should be perpendicular to the direction of velocity.

Correct answer: B̅ should be perpendicular to the direction of velocity and E̅ should be along the direction of velocity.

Solution

For the particle to move in a horizontal direction without deviation, the magnetic force (qvB) and electric force (qE) must cancel each other. This requires the magnetic field to be perpendicular to the velocity and the electric field to be along the velocity, ensuring no net force acts perpendicular to the motion.

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