Question

Calculate the ratio of electric to gravitational force between two electrons.

Answer 1

Hint:The electrostatic force is related to the magnitudes of the charges of interacting items, while the gravitational force is proportional to the masses of interacting objects. As a result, both forces are proportional to an interaction strength attribute for a particular field. We can determine the ratio if we know their equations.

Complete step by step answer:
An electric force is the repulsive or attractive interaction between any two charged things.Newton's equations of motion define the impact and effects of any force on a particular body, just as they do for any other force. The electric force is one of the many forces that exert themselves on things. Gravity, or gravitation, is a natural phenomena that causes all things with mass or energy to gravitate toward one another, including planets, stars, galaxies, and even light. Gravity gives tangible items weight on Earth, while the Moon's gravity creates ocean tides.

Electric force of an electron is given as ${\displaystyle \frac{e^2}{4\pi {\epsilon }_o{r}^2}}$
Where $e$ = charge of an electron $1.6\times {10}^{-19}C$
${\displaystyle \frac{1}{4\pi {\epsilon }_o}}$= unit of permittivity $9\times {10}^9{\displaystyle \frac{N{m}^2}{C^2}}$
Also the gravitational force of an electron is given as ${\displaystyle \frac{G{(m_e)}^2}{r^2}}$
Where $G$ = universal gravitational constant $6.67\times {10}^{-11}{\displaystyle \frac{N{m}^2{g}^2}{k}}$
$m_e$ is the mass of the electron = $9.1\times {10}^{-31}kg$
By dividing the 2 equations we can get
Ratio = ${\displaystyle \frac{e^2}{4\pi {\epsilon }_{o}G{(m_e)}^2}}$
Now by substituting all the values of given terms we get
$R={\displaystyle \frac{9\times {10}^9{\displaystyle \frac{N{m}^2}{C^2}}\times {\left(1.6\times {10}^{-19}C\right)}^2}{6.67\times {10}^{-11}{\displaystyle \frac{N{m}^2}{k}}{g}^2\times {\left(9.1\times {10}^{-31}kg\right)}^2}}$
$\therefore R=4.17\times {10}^{42}$

Hence, the ratio of electric to gravitational force between two electrons is $4.17\times {10}^{42}$.

Note: Try to keep in mind all the values mentioned here like mass of electron etc., Ratio is unitless so final answer contains no unit. For circumstances involving point charges and/or simple symmetric geometries such as lines or spheres of charge, Coulomb's Law is an appropriate choice.