Coulomb's law
Electric Fields - OCR A-Level Physics
Key Definition
Coulomb's law
The force between two point charges is proportional to the product of their charges and inversely proportional to the square of the distance between them.
The force between two point charges is proportional to the product of their charges and inversely proportional to the square of the distance between them.
$$F = \frac{Q_1 Q_2}{4\pi\epsilon_0 r^2}$$
- Like charges repel (F is positive); unlike charges attract (F is negative, by convention).
- Coulomb's lawThe electrostatic force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. applies to point chargesCharged objects treated as if all charge is concentrated at a single point; valid when separation ≫ size. or to charged spheres treated as point charges at their centres.
- The force obeys an inverse-square lawA relationship in which a physical quantity is inversely proportional to the square of the distance from its source., just like Newton's law of gravitationThe gravitational force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them..
- The constant $\frac{1}{4\pi\epsilon_0}$ $\approx 8.99$ $\times 10$^$9 \text{ N m}$^$2 \text{ C}^{-2}.$
Common Mistake
MEDIUM
Wrong: Using diameter instead of centre-to-centre distance for r in Coulomb's lawThe electrostatic force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them..
Right: r is always the distance between the centres of the charges, not the gap between surfaces. For conducting spheres, chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). resides on the surface but r is measured centre-to-centre.
Right: r is always the distance between the centres of the charges, not the gap between surfaces. For conducting spheres, chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). resides on the surface but r is measured centre-to-centre.