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Q. 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 $10^{5} ms ^{-1}$ 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) $\vec{B}$ should be perpendicular to the direction of velocity and $\vec{E}$ should be along the direction of velocity
(2) Both $\vec{B}$ and $\vec{E}$ should be along the directionof velocity
(3) Both $\vec{B}$ and $\vec{E}$ are mutually perpendicular and perpendicular to the direction of velocity.
(4) $\vec{B}$ should be along the direction of velocity and $\vec{E}$ should be perpendicular to the direction of velocity
Which one of the following pairs of statements is possible?

AIPMTAIPMT 2010Moving Charges and Magnetism

Solution:

Both $\vec{B}$ and $\vec{E}$ should be along the direction of velocity and both $\vec{B}$ and $\vec{E}$ are mutually perpendicular and perpendicular to the direction of velocity.