Question

How much stronger is the electric force between two

protons than the gravitational force between them?

Answer 1

Step-by-step explanation:

The electric force between two protons is 10^36 times stronger than the gravitational force between them.

Answer 2

Electric force is 1.23 x 10³⁶ times stronger than gravitational force.

Step-by-step explanation:

First, we will calculate the gravitational force using Newton's Law:

`F_G = (Gm^2)/(r^2)\\\\`

where,

F_G = Gravitational Force = ?

G = Gravitational Constant = 6.67 x 10⁻¹¹ Nm²/kg²

m = mass of proton = 1.67 x 10⁻²⁷ kg

r = distance between protons

Therefore,

`F_G = ((6.67\ x\ 10^(-11)\ Nm^2/kg^2)(1.67\ x\ 10^(-27)\ kg)^2)/(r^2)\\\\F_G = (1.86\ x\ 10^(-64)\ Nm^2)/(r^2)\\\\`

Now, we will calculate the electrostatic force using Colomb's Law:

`F_E = (kq^2)/(r^2)\\\\`

where,

F_E = Electrostatic Force = ?

k = Colomb's Constant = 9 x 10⁹ Nm²/C²

q = charge of proton = 1.6 x 10⁻¹⁹ C

r = distance between protons

Therefore,

`F_E = ((9\ x\ 10^(9)\ Nm^2/kg^2)(1.6\ x\ 10^(-19)\ C)^2)/(r^2)\\\\F_E = (2.3\ x\ 10^(-28)\ Nm^2)/(r^2)\\\\`

Dividing both forces:

`(F_E)/(F_G) = (2.3\ x\ 10^(-28))/(1.86\ x\ 10^(-64))`

F_E = 1.23 x 10³⁶ F_G

Therefore, electric force is 1.23 x 10³⁶ times stronger than gravitational force.