Compare Gravitational and Electric Forces - Physics

Direction is unchanged (still attractive or still repulsive). Product $q_1q_2$ stays same sign when both flip.

$F_g$ doubles. Force is directly proportional to each mass.

They become $\frac{1}{9}$ as large. Inverse-square law: tripling $r$ gives $F\propto\frac{1}{(3r)^2}=\frac{1}{9r^2}$.

They become $\frac{1}{4}$ as large. Inverse-square law: doubling $r$ gives $F\propto\frac{1}{(2r)^2}=\frac{1}{4r^2}$.

Electric; $\frac{F_e}{F_g}\approx 10^{42}$ for two electrons. Electric force vastly exceeds gravity for elementary particles.

Electric; $\frac{F_e}{F_g}\approx 10^{36}$ for two protons. Electromagnetic force dominates at atomic scales.

Electric force can be attractive or repulsive. Like charges repel, opposite charges attract.

Gravitational force is always attractive. Masses always attract; no negative mass exists.

Both follow an inverse-square law: $F\propto \frac{1}{r^2}$. Force decreases with square of distance for both interactions.

$k:\ \text{N}\cdot\text{m}^2/\text{C}^2$. Coulomb's constant has units of force×area per charge squared.

$G:\ \text{N}\cdot\text{m}^2/\text{kg}^2$. Gravitational constant has units of force×area per mass squared.

$\frac{F_e}{F_g}=\frac{k|q_1 q_2|}{G m_1 m_2}$. Ratio cancels $r^2$ terms, leaving charge and mass factors.

$F_e = k\frac{|q_1 q_2|}{r^2}$. Coulomb's law gives force between point charges.

$F_g = G\frac{m_1 m_2}{r^2}$. Newton's law of universal gravitation for point masses.

$F_e$ doubles. Force is directly proportional to each charge magnitude.

No; $\frac{F_e}{F_g}$ is independent of $r$. Both forces have same $r^2$ dependence, which cancels in ratio.

$\frac{F_e}{F_g}=\frac{k q^2}{G m^2}$. Simplifies since $q_1=q_2=q$ and $m_1=m_2=m$.

Direction reverses (attractive becomes repulsive or vice versa). Product $q_1q_2$ changes sign when only one flips.

$G\approx 6.67\times 10^{-11}$, $k\approx 8.99\times 10^9$. Values show $k\gg G$ in SI units.

Along the line joining them; toward unlike, away from like. Electric forces act along the line between charges with direction based on sign.

$\mathrm{N,m^2/C^2}$. Similar to $G$ but with charge (coulombs) instead of mass (kg).

$\frac{F_e}{F_g}=\frac{kq^2}{Gm^2}$. Simplifies when charges and masses are equal, showing dependence on $\frac{q}{m}$ ratio.

No change; $\frac{F_e}{F_g}$ stays the same. Ratio cancels the factor of 2 in both numerator and denominator.

$F_e\gg F_g$ (by about $10^{36}$ to $10^{39}$). Electric forces dominate by many orders of magnitude at particle scale.

$\frac{F_e}{F_g}\approx10^{39}$. Even larger ratio for electron-proton due to electron's tiny mass.

$\frac{F_e}{F_g}\approx10^{36}$. Electric force dominates at atomic scale due to large charge-to-mass ratio.

$F_g=G\frac{m_1m_2}{r^2}$. Newton's law of universal gravitation with inverse square dependence on distance.

Each becomes $\frac{1}{4}$ of its original value. Both forces have $\frac{1}{r^2}$ dependence, so doubling $r$ gives $\frac{1}{2^2}=\frac{1}{4}$.

Each becomes $\frac{1}{9}$ of its original value. Tripling distance gives $\frac{1}{3^2}=\frac{1}{9}$ due to inverse square law.