Question

A charged cloud system produces an electric field in the air near the earths surface. A particle of charge $-2\times 10^{-9}C$ is acted on by a downward electrostatic force of $3\times 10^{-6}N$ when placed in this field. The gravitational and electrostatic force, respectively, exerted on a proton placed in this field are

• A. $1.64\times 10^{-26}N,2.4\times 10^{-16}N$
• B. $1.64\times 10^{-26}N,1.5\times 10^{-3}N$
• C. $1.56\times 10^{-18}N,2.4\times 10^{-16}N$
• D. $1.5\times 10^{-3}N,2.4\times 10^{-16}N$

Answer 1

Answer: (A)

For electrostatic force, $F=\frac{1}{4\pi {\epsilon }_0}\times \frac{q_1{q}_2}{r^2}3\times 10^{-6}$
$=\frac{9\times 10^9\times 2\times 10^{-9}\times 2\times 10^{-9}}{r^2}$
$\therefore r^2=\frac{9\times 10^9\times 2\times 10^{-9}\times 2\times 10^{-9}}{3\times 10^{-6}}$
Electrostatic force, when proton placed in this field,
$F=\frac{1}{4\pi {\epsilon }_0}\times \frac{\text{ Charge of partice }\times \text{ charge of proton }}{r^2}$
$F=\frac{\frac{9\times 10^9\times 2\times 10^{-9}\times 1.6\times 10^{-19}}{9\times 10^9\times 2\times 10^{-9}\times 2\times 10^{-9}}}{3\times 10^{-6}}$
$F=2.4\times 10^{-16}N$
Similarly, we can calculate gravitational force
$=1.64\times 10^{-26}N$