Question

Find the ratio of the magnitude of the electric force to the gravitational force acting between two protons.

Answer 1

We know,

Charge on one proton (q) = $1.6\times {10}^{-19}C$

Mass of the one proton (m) = $1.67\times {10}^{-27}kg$

Let the distance between two protons = r

Then

Electric force between them is given as

$f_e=\frac{1}{4\pi {\in }_0}\times \frac{q^2}{r^2}$

Gravitational force between them is given as

$F_g=\frac{Gq{m}^2}{r^2}$

Now finding the ration of electric force to the gravitational force

$\therefore \frac{F_3}{F_g}=\frac{1}{4\pi {\in }_0}\times \frac{q^2}{r^2}\times \frac{r^2}{G{m}^2}$

$=\frac{9\times {10}^9\times 1.6\times 1.6\times {10}^{-38}}{6.67\times {10}^{-11}\times 1067\times 1067\times {10}^{-54}}$

After solving

$\frac{F_e}{F_g}=1.24\times {10}^{36}$

Hence ratio is $1.24\times {10}^{36}$