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 ${10}^{5}m{s}^{-1}$ 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

(i) $\overrightarrow{B}$ should be perpendicular to the direction of velocity and $\overrightarrow{E}$ should be along the direction of velocity.
(ii) Both $\overrightarrow{B}$ and $\overrightarrow{E}$ should be along the direction of velocity.

(iii) Both $\overrightarrow{B}$ and $\overrightarrow{E}$ are mutually perpendicular and perpendicular to the direction of velocity.
(iv) $\overrightarrow{B}$ 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

• A. (i) and (iii)
• B. (iii) and (iv)
• C. (ii) and (iii)
• D. (ii) and (iv)

Answer 1

The correct option is C (ii) and (iii)

Case 1:- In figure 1 if $F_E=F_B$ $\Rightarrow$ particle will always move in a straight line.(option (iii))
Case 2:- In figure 2 particle will always move in a straight line.(option (ii))