Question

show that electrostatic force is about 36 orders of magnitude stronger than gravitational force​

Answer 1

To show:

Electrostatic force is about 36 orders of magnitude stronger than gravitational force.

Calculation:

Let's consider 2 protons:

So, electrostatic force:

$F_{e} = \dfrac{k {q}^{2} }{ {r}^{2} }$

$\implies F_{e} = \dfrac{9 \times {10}^{9} \times {(1.6 \times {10}^{ - 19} )}^{2} }{ {r}^{2} }$

Now, gravitational force between the protons:

$F_{g} = \dfrac{G {m}^{2} }{ {r}^{2} }$

$F_{g} = \dfrac{6.67 \times {10}^{ - 11} \times {(1.67 \times {10}^{ - 27} )}^{2} }{ {r}^{2} }$

So, the ratio:

$\therefore \dfrac{F_{e}}{F_{g}} = \dfrac{9 \times {10}^{9} \times {(1.6 \times {10}^{ - 19} )}^{2} }{6.67 \times {10}^{ - 11} \times {(1.67 \times {10}^{ - 27} )}^{2} }$

$\implies\dfrac{F_{e}}{F_{g}} = 1.23 \times {10}^{36}$

$\boxed{ \bf \implies \: F_{e} = (1.23 \times {10}^{36} ) \times F_{g}}$

[Hence proved]