A particle having a mass of $10^{- 2}$ kg carries a charge of 5 $\times$ 10^-6C. The particle is given an initial horizontal velocity of $5 \times 10^{- 8} \frac{m}{s}$ in the presence of electric field $\vec{E}$ and magnetic field $\vec{B}$ . To keep the particle moving in a horizontal direction, it is necessary that
( 1 ) B should be perpendicular to the direction of velocity and E should be along the direction of velocity.
( 2 ) Both B and E should be along the direction of velocity.
( 3 ) Both B and E are mutually perpendicular and perpendicular to the direction of velocity.
(4) E should be perpendicular to the direction of velocity.
Which one of the following pairs of statements is possible?

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(2) and (4)

(3) and (4)

(2) and (3)

(1) and (3)

answer is D.

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Detailed Solution

Force due to electric field acts along the direction of the electric field but force due to the magnetic field acts along a direction perpendicular to both the velocity of the charged particle and the magnetic field. Hence both statements (2) and (3) are true. In statement (2), magnetic force is zero, so, electric force will keep the particle continue to move in horizontal direction. In statement (3), both electric and magnetic forces will be opposite to each other. If their magnitudes will be equal then the particle will continue horizontal motion.

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