Respuesta :
This is the answer tab
Firstly, we need to write the formulas for both the gravitational force and electric force. Our gravitational force is:
[tex]F_g=G\frac{m_1m_2}{d^2}[/tex]And the electric force is:
[tex]F_e=k\frac{q_1q_2}{d^2}[/tex]We can see that these forces have almost equal formulas. What we want is Fe/Fg. Before this, we can simplify the forces, as both particles have the same charge and mass. We're left with the following:
[tex]F_g=G\frac{m^2}{d^2}[/tex]And
[tex]F_e=k\frac{q^2}{d^2}[/tex]By dividing both, we get
[tex]\frac{F_e}{F_g}=\frac{(\frac{kq^2}{d^2})}{(\frac{Gm^2}{d^2})}=\frac{kq^2}{d^2}*\frac{d^2}{Gm^2}[/tex]We have d^2 on the numerator and denominator. We can elimante the distance then, as it is different from zero. We have the following:
[tex]\frac{F_e}{F_g}=\frac{kq^2}{Gm^2}[/tex]We can then replace our values with the constants. k is Coulomb's constant, q is the charge of a proton, G is Newton's constant, and m is the mass of a proton. We finally get
[tex]\frac{F_e}{F_g}=\frac{(9*10^9)*(1.6*10^{-19})^2}{(6.67*10^{-11})*(1.67*10^{-27})^2}=1.2386*10^{36}[/tex]So, the electric force is 1.2386*10^36 times higher than the gravitational. The most interesting about this, is that it doesn't depend on the distance the two of them are apart.
