A charged particle of mass m = 2 kg and charge 1μC is projected from a horizontal ground at

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1. Electric Charges and Fields

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A charged particle of mass $m = 2\ kg$ and charge $1μC$ is projected from a horizontal ground at an angle $\theta = 45^o$ with speed $10\ ms^{-1}$ . In space, a horizontal electric field towards the direction of projection $E = 2 \times 10^7\ NC^{-1}$ exists. The range of the projectile is......$m$

A

$20$

B

$60$

C

$200$

D

$180$

Solution

$a_{x}=\frac{q E}{m}=\frac{10^{-6} \times 2 \times 10^{7}}{2}=10 \,m s^{-2}$

Time of flight $\mathrm{T}=\frac{2 \mathrm{u} \sin \theta}{\mathrm{g}}=\frac{2 \times 10 \times \frac{1}{\sqrt{2}}}{10}$

$T=\sqrt{2}\, \sec$

Hence, range ${\rm{R}} = {{\rm{u}}_{\rm{x}}}{\rm{T}} + \frac{1}{2}{{\rm{a}}_{\rm{x}}}{{\rm{T}}^2}$

$\mathrm{R}=10 \cos 45^{\circ} \times \mathrm{T}+\frac{1}{2} \mathrm{a}_{\mathrm{x}} \mathrm{T}^{2}$

$=\frac{10}{\sqrt{2}} \sqrt{2}+\frac{1}{2} \times 10 \times 2$

$\Rightarrow R=20 \mathrm{\,m}$

Standard 12

Physics

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