Question

Given the following data, calculate the electrostatic force and gravitational force between two electrons. Show that the electrostatic force is much greater than the gravitational force for the electrons separated by a certain distance.
Charge on the electron $=1.6\times {10}^{-19}C$
Mass of the electron $=9.1\times {10}^{-31}kg$
Gravitational constant $=6.67\times {10}^{-11}N{m}^{2}k{g}^{-2}$

Answer 1

given,

charge on the electron$=1.6\times {10}^{-19}C$

mass of the electron$=9.1\times {10}^{-31}kg$

gravitational constant$=6.67\times {10}^{-11}N{m}^{2}k{g}^{-2}$

i)to find the electrostatic force b/w 2 electron.

let 2 electrons are at a distance 'd' apart

the electrostatic force is $F_e=\frac{1}{4\pi {\epsilon }_o}\frac{q^2}{d^2}=\frac{9\times {10}^9\times {(1.6\times {10}^{-19})}^2}{d^2}=\frac{23.04\times {10}^{-29}}{d^2}N$

ii) To find the gravitational force,

$F_g=\frac{{Gm}^2}{d^2}=\frac{6.67\times {10}^{-11}\times {(9.1\times {10}^{-31})}^2}{d^2}=\frac{553.56\times {10}^{-73}}{d^2}N$

iii) to show that electrostatic force is much grater then gravitational force.

for this we take ratio $\frac{F_e}{F_g}=\frac{23.04\times {10}^{-29}}{553.56\times {10}^{-73}}=0.0416\times {10}^{44}=0.416\times {10}^{43}$

we can see tham $f_e>>f_g$ ie. electrostatice force is much grater than the gravitational force for $2$ electrons separated by a certain distance