A particle of mass $1 \times 10^{- 26}$ kg and charge $+ 1.6 \times 10^{- 19}$ C travelling with a velocity of $1.28 \times 10^{6}$ m/s along positive direction of $x$ -axis enters a region in which a uniform electric field $E$ and a uniform magnetic field $B$ are present such that
$E_{z} = - 102.4 k V / m$ and $B_{y} = 8 \times 10^{- 2} W b / m^{2}$
The particle enters this region at origin at time $t = 0$ . Then,

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net force acts on this particle along the +ve z-direction

net force acts on this particle along the -ve z-direction

net force acts in xz-plane

net force acting on particle is zero

answer is C.

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Detailed Solution

$F_{e} = q E = (1.6 \times 10^{- 19}) (- 102.4 \times 10^{3}) \hat{k} = (- 1.6384 \times 10^{- 14} \hat{k}) N F_{m} = q (v \times B) = (1.6 \times 10^{- 19}) [(1.28 \times 10^{6} \hat{i}) \times (8 \times 10^{- 2} \hat{j})] = (1.6384 \times 10^{- 14} \hat{k}) N$