The Basic Forces and Messenger Particles — Question 8

Question 8

Electric repulsion overwhelms gravity between two protons

Compare $F_E=ke^2/r^2$ and $F_G=Gm_p^2/r^2$. Use $k=8.99\times10^9$, $e=1.60\times10^{-19}$ C, $G=6.67\times10^{-11}$ SI and $m_p=1.67\times10^{-27}$ kg.

1. Find the force ratio and show that it is independent of separation.

2. Find the mass m of two particles of charge +e for which these two classical forces would have equal magnitude.

Question 8 - Solution

Electric repulsion overwhelms gravity between two protons

(a) Method and calculation

$$\frac{F_E}{F_G}=\frac{ke^2}{Gm_p^2}.$$$$\boxed{F_E/F_G=1.23720\times10^{36}}.$$

(b) Interpretation and further calculation

$$Gm^2=ke^2\Rightarrow m=e\sqrt{k/G}.$$$$\boxed{m=1.85753\times10^{-9}\ {\mathrm{kg}}}.$$

Physical check

This is a classical comparison of pair forces, not a proposed elementary particle or a statement about collective neutral matter.