Forces of Nature

• gravity
• electromagnetism
• weak force
  • radioactivity
• strong force
  • keeps together protons and neutrons

Gravity §

$$F_g=\frac{G{m}_1{m}_2}{r^2}$$

Electricity and Magnetism §

$$F_e=\frac{k{q}_1{q}_2}{r^2},k=8.988\cdot 10^9\frac{Nm}{C^2}$$

Plugging in units for dimensional analysis to verify answer fails when combining gravity and electromagnetic force for 2 electrons

$$|\frac{F_g}{F_e}|=\frac{G{m}_e^2}{k{q}_e^2}\sim 10^{-43}$$

Effective Force §

Consider system w/ equilibrium point: for some $x=0$, $F(x=0)=0$.