Gravity vs. Electric Fields
Comparing the two fields, plus mixed practice
Do Now: A small magnet or a charged balloon can lift a paper clip or bits of paper off the floor — beating the gravity of the entire Earth. What does that tell you?
Gravity is by far the weakest of these forces. It only wins on large scales because mass always adds up, while positive and negative charges usually cancel.
A. Side by Side
| Gravitational Field | Electric Field | |
|---|---|---|
| Caused by | Mass | Charge |
| Field strength | g = Fg/m (N/kg) | E = Fe/q (N/C) |
| Force law | Fg = Gm1m2/r² | Fe = kq1q2/r² |
| Distance | Inverse square | Inverse square |
| Attract or repel? | Always attracts | Opposites attract, likes repel |
| Field lines | Point toward the mass | Point away from + and toward − |
| Strength | Very weak | Very strong |
B. How Much Stronger?
In a hydrogen atom, the electron and proton are 5.3 × 10−11 m apart. Compare the electric and gravitational forces between them.
k = 8.99 × 109 N•m²/C², e = 1.60 × 10−19 C, mp = 1.67 × 10−27 kg, me = 9.11 × 10−31 kg
Fe = (8.99 × 109)(1.60 × 10−19)2(5.3 × 10−11)2 = 8.2 × 10−8 N
Fg = (6.67 × 10−11)(1.67 × 10−27)(9.11 × 10−31)(5.3 × 10−11)2 = 3.6 × 10−47 N
The electric force is about 2 × 1039 times stronger!
Planets and stars have nearly equal amounts of positive and negative charge, so their electric forces cancel. Mass is always positive, so gravity keeps adding up.
Explore
Drag the test mass around the planet. Change the planet and the mass.
C. Mixed Practice
Both fields follow an inverse square law. If the distance from a mass or charge triples, what happens to the field strength?
It becomes 1/9 as strong.
A 0.50-kg rock and a 0.50-C charge each feel a 4.9-N force. Find g and E.
g = 4.9/0.50 = 9.8 N/kg; E = 4.9/0.50 = 9.8 N/C
Name one way gravitational and electric fields are alike and one way they are different.
Alike: both get weaker with the square of distance (or both exert forces without contact). Different: gravity only attracts; electric forces can attract or repel.
Draw the field lines for a planet and for a positive charge. How are they different?
Planet: lines point inward, toward the mass. Positive charge: lines point outward, away from the charge.
Check Your Understanding
5 quick questions — pick an answer to see if you’re right.
1. Which is the unit of electric field strength?
2. Which statement is true for gravitational fields but NOT electric fields?
3. Compared with gravity, the electric force between a proton and electron is
4. If the distance from a charge is cut in half, the electric field becomes
5. Gravity controls the motion of planets because