Electricity and Magnetism

Mathematical Tools and Fields

01Series Approximations: Keeping One or Two Terms 02Integrals as Sums: Along a Line and a Curved Path 03Line Integrals: Work as the Integral of F · ds 04Closed Line Integrals: Work Around a Loop 05Double Integrals: Area, Charge and Volume 06Closed Surface Integrals: The Sphere and Its Charge 07Electric Flux Through Surfaces and Volume Integrals Problem set0/10 Problem set 20/10 MIT problem set0/4

01Field Theory Versus Action at a Distance 02Scalar Fields: Contour, Color and Relief Maps 03Vector Fields, Sources, Sinks and Divergence 04Curl: Measuring the Circulation of a Field 05Gravitational, Electric and Magnetic Fields 06Drawing Vector Fields: Arrows, Lines and Grass Seeds Problem set0/10 Problem set 20/10 MIT problem set0/1

Electrostatics

01Coulomb's Law: Force Between Two Point Charges 02Superposition: Adding Coulomb Forces as Vectors 03Field Lines, Null Points and Uniform Fields 04The Electric Dipole and Its 1/r³ Field 05Torque, Energy and Force on a Dipole in a Field Problem set0/10 Problem set 20/10 MIT problem set0/1

Coulomb's Law: Force Between Two Point Charges

Why does the force between two point charges fall off as 1/r², and how does Coulomb's law fix its direction?

Loading…

←Previous Drawing Vector Fields: Arrows, Lines and Grass Seeds Next Superposition: Adding Coulomb Forces as Vectors →

Your summary note

1. Two kinds of charge, quantization and conservation
  Record Franklin's sign convention, that like charges repel and opposite charges attract, the value $e = 1.602 \times 10^{-19}$ C, and the statements that charge comes in multiples of $e$ and is conserved.
2. Coulomb's law $\vec{F}_{12} = k_e \frac{q_1 q_2}{r^2}\hat{r}$
  Write the vector law with $\hat{r}$ pointing from $q_1$ to $q_2$ , state $\vec{F}_{21} = -\vec{F}_{12}$ , and sketch the like-sign and opposite-sign cases showing how the sign of $q_1 q_2$ sets the direction.
3. The Coulomb constant and the permittivity of free space
  Write $k_e = 1/(4\pi\varepsilon_0) = 8.9875 \times 10^9\ \text{N} \cdot \text{m}^2/\text{C}^2$ , compute $\varepsilon_0 = 1/(\mu_0 c^2)$ from $\mu_0 = 4\pi \times 10^{-7}$ and $c$ , and carry the units to $\text{C}^2/(\text{N} \cdot \text{m}^2)$ .
Attempt 1 of 2