Advanced · 14 min
Electric forces and fields
Calculate electrostatic force magnitudes and connect field strength to force on charge.
Forces between charges
For stationary point charges in vacuum, Coulomb's law gives force magnitude F = k × |q₁q₂| ÷ r², with k approximately 9 × 10⁹ N·m²/C². Like charges repel and unlike charges attract. Convert microcoulombs to coulombs: 1 μC = 10⁻⁶ C. Distance is measured between the charges. As with gravity, doubling distance reduces the force magnitude to one quarter when the charges are unchanged.
Worked example
Two charges of 1 μC and 2 μC are 1 m apart. Force magnitude = 9 × 10⁹ × 10⁻⁶ × 2 × 10⁻⁶ = 0.018 N
A field describes the surroundings
Electric field strength is force per unit positive test charge: E = F ÷ q. Its unit is N/C. Field direction is the direction of force on a positive charge; a negative charge feels force in the opposite direction. The test charge should be small enough not to disturb the source charges significantly. To find force magnitude in a given field, use |F| = |q| × E.
Worked example
A positive charge of 2 μC feels a force of 0.01 N. Field strength = 0.01 ÷ (2 × 10⁻⁶) = 5,000 N/C
Compare charge and distance changes
- Starting with a force magnitude of 0.02 N between two point charges, find the new magnitude if their separation doubles.
- Return to the original separation and double one charge instead. Calculate the new force and state how changing a charge's sign affects the force direction.