Comparing Gravitational and Electric Fields

1. Both follow inverse square laws: $F \propto 1/r^2$
2. Both have radial fields around point sources
3. Both have $g$ or $E$ = $-dV/dr$
4. Both have $F = 0$ and $V = 0$ at infinity
5. Both are conservative (path-independent work)

1. Gravity always attracts — electric can attract or repel
2. Gravitational potential always negative — electric can be positive or negative
3. Cannot shield gravity — electric fields can be shielded (Faraday cage)
4. Gravity acts on mass — electric acts on charge
5. Much weaker: $F_\text{grav}$ between two protons is $\sim 10^{36}$ times smaller than $F_\text{elec}$

• Lines/surfaces of constant potential
• Always perpendicular to field lines
• No work done moving along an equipotential
• Closer equipotentials = stronger field

For uniform fields:

• Gravitational: horizontal equipotentials (near Earth surface)
• Electric: parallel equipotentials between parallel plates

For radial fields:

• Concentric circles/spheres around the source

Compare the gravitational and electric forces between two protons at separation $10^{-15}$ m.

$F_g = Gm^2/r^2 = 6.67 \times 10^{-11} \times (1.67 \times 10^{-27})^2/(10^{-15})^2 = 1.86 \times 10^{-34}$ N

$F_e = ke^2/r^2 = 8.99 \times 10^9 \times (1.6 \times 10^{-19})^2/(10^{-15})^2 = 230$ N

Ratio: $F_e/F_g = 230/1.86 \times 10^{-34} = 1.2 \times 10^{36}$

Gravity is utterly negligible at the atomic scale!

• Both fields: inverse square, conservative, $F_{\text{str}} = -dV/dr$
• Gravity: always attractive, potential always negative, much weaker
• Electric: can attract or repel, potential can be ±, can be shielded