Question

A charged particle of mass $m=2kg$ and charge $1\mu C$ is thrown from a horizontal ground at an angle of ${45}^{\circ }$ with the horizontal with a speed of 10 m/s. In space a horizontal electric field $E=2\times {10}^7$ N/C exists. Find the range of the projectile.

Answer 1

Acceleration of particle along x-axis is $a_x$
Given $E=2\times {10}^7,m=2\text{kg},q={10}^{-6}C$
Force by electric field on charge
$F=qE$
By Newton's second law
$F=ma$
$a_x=\frac{F}{m}=\frac{qE}{m}$
$=\frac{{10}^{-6}\times 2\times {10}^7}{2}$
$=10m/s^2$

Given $u=10m{s}^{-1}$
$\sin \theta =\sin {45}^{\circ }=\frac{1}{\sqrt{2}},$ and $T$ is time period
Time of flight $T=\frac{2u\sin \theta }{g}=\frac{2\times 10\times \frac{1}{\sqrt{2}}}{10}=\sqrt{2}s$...(2)
Range of the particle can be given by second equation of motion
$R=u_{x}T+\frac{1}{2}{a}_x{T}^2$
$R=10\cos {45}^{\circ }\times T+\frac{1}{2}{a}_x{T}^2$
$R=\frac{10}{\sqrt{2}}\times \sqrt{2}+\frac{1}{2}\times 10\times 2=20m$
Hence, option (d) is correct.