Two electrons are separated by one cm. What is the ratio of the electric force to the gravitational force between them?

Note that Me = 9.11 x 10^-31kg, Ke=8.99 x 10^9 N m^2/ C^2 , G= 6.67 x 10^-11 N m^2/kg^2, e=1.6 x 10^-19 C, and Fg = G m1xm2/r^2

a)2.3 x 10^2
b) 1.3 x 10^20
c)3.1 x 10^22
d)4.2 x 10^42

The ratio of the electric force to the gravitational force between them is d. 4.2 × 10⁴²

The electric force between the two electrons according to Coulomb's law is F = ke²/r² where

Also, the gravitational force between the electrons according to Newton's law of gravitation is f = GMe²/r² where

Since we want to find the ratio between the electric force and the gravitational force, we have F/f = ke²/r² ÷  GMe²/r²

= ke²/GMe²

Substituting the values of the variables into the equation, we have

ke²/GMe² = 8.99 × 10⁹ Nm²/C² × (1.6 × 10⁻¹⁹ C)²/[6.67 × 10⁻¹¹ Nm²/kg² × (9.11 × 10⁻³¹ kg)²]

= 8.99 × 10⁹ Nm²/C² × 2.56 × 10⁻³⁸ C²/[6.67 × 10⁻¹¹ Nm²/kg² × 82.9921 × 10⁻⁶² kg²]

= 23.0144 × 10⁻²⁹ Nm²/553.557307 × 10⁻⁷³ Nm²

= 0.0416 × 10⁴⁴

= 4.16 × 10⁴²

≅ 4.2 × 10⁴²

So, the ratio of the electric force to the gravitational force between them is d. 4.2 × 10⁴².

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d)

Explanation:

We are given that

By using 100cm=1 m

Electric force=

Using the formula

Gravitational force,

Using the formula

Option d is true.

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