$(a)\;200m\qquad(b)\;164 m\qquad(c)\;56 m\qquad(d)\;40 m$

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Answer : (a) 56 m

Explanation :

The path of the particle will be a parabola , but along x - axis also motion of the particle will be accelerated . Time of flight of particle is

$T=\large\frac{2u_{y}}{g}=\large\frac{2\times20 cos 45^{0}}{10}=2 \sqrt{2} s$

Horizontal range R = $\;u_{x} T + \large\frac{1}{2} a_{x} T^{2}$

$a_{x}=\large\frac{qE}{m}=\large\frac{2\times2\times10^{-6}\times10^{6}}{1}$

$=4 m/s^{2}$

$R=(20 \large\frac{1}{\sqrt{2}})\;(2 \sqrt{2})+\large\frac{1}{2}\times4\times8$

$=40+16$

$=56 m$

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