A particle having a mass of 10$-$2 kg carries a charge of 5 $ \times $ 10$-$8 C. The particle is given an initial horizontal velocity of 105 m s$-$1 in the presence of electric field $\overrightarrow E $ and magnetic field $\overrightarrow B $. To keep the particle moving in a horizontal direction, it is necessary that (1) $\overrightarrow B $ should be perpendicular to the direction of velocity and $\overrightarrow E $ should be along the direction of velocity (2) Both $\overrightarrow B $ and $\overrightarrow E $ should be along the direction of velocity (3) Both $\overrightarrow B $ and $\overrightarrow E $ are mutually perpendicular and perpendicular to the direction of velocity. (4) $\overrightarrow B $ should be along the direction of velocity and $\overrightarrow E $ should be perpendicular to the direction of velocity Which one of the following pairs of statements is possible ?

Question

A particle having a mass of 10^$-$2 kg carries a charge of 5 $ \times $ 10^$-$8 C. The particle is given an initial horizontal velocity of 10⁵ m s^$-$1 in the presence of electric field $\overrightarrow E $ and magnetic field $\overrightarrow B $. To keep the particle moving in a horizontal direction, it is necessary that
(1)  $\overrightarrow B $ should be perpendicular to the direction of velocity and $\overrightarrow E $ should be along the direction of velocity

(2)  Both $\overrightarrow B $ and $\overrightarrow E $ should be along the direction of velocity

(3)  Both $\overrightarrow B $ and $\overrightarrow E $ are mutually perpendicular and perpendicular to the direction of velocity.

(4)  $\overrightarrow B $ should be along the direction of velocity and $\overrightarrow E $ should be perpendicular to the direction of velocity

Which one of the following pairs of statements is possible ?

(1) and (3)

(3) and (4)

(2) and (3)

(2) and (4)

Solution

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