Chapter 3 · Section 3.1
3.1 Coulomb's Law and the Electric Field
Coulomb's experimental force law between charges at rest, superposition and the electric field it leads to, field lines, the step-by-step calculation of the field of line, surface and volume charges, and six engineering devices that use the Coulomb force.
- which few experimental facts the whole of electrostatics is built on,
- how to describe charge: point charges and line, surface and volume densities,
- how to use Coulomb's law in vector form, with the vector from the source to the field point,
- how forces and fields of many charges add (superposition), and what the electric field is,
- how to compute of a continuous distribution step by step, using symmetry to save work, and
- how to read and draw field lines, and how six engineering devices use the Coulomb force.
Rub a balloon on your hair and it sticks to the wall. A photocopier puts black powder exactly where the letters are. A power station cleans tonnes of ash from its smoke without any filter cloth. A spark jumps from your finger to a door handle in winter, and the same spark can quietly destroy a microchip. All of these are the same force at work: the electric force between charges at rest.
In this section we meet that force. We begin with the short list of experimental facts on which the whole course rests, describe what electric charge is and how we write it down, and state Coulomb's law. Adding the forces of many charges (superposition) then leads us to the most important idea of the subject, the electric field. Throughout, we shall keep asking two simple questions: where is the charge? and where do we want to know its effect? With the answers written as vectors, every calculation in this section becomes the same short recipe.
Contents of Section 3.1
Start reading →- 3.1.1Fundamental assumptions
- 3.1.2The notion of charge
- 3.1.3Coulomb's law
- 3.1.4Applications of Coulomb's law
- 3.1.5The superposition principle
- 3.1.6The electric field
- 3.1.7Field lines
- 3.1.8Superposition of the electric field
- 3.1.9Recap
- 3.1.10Problems and solutions
Problems · 3
Home exercises · 4
Further exercises · 10
- Exercise 3.1.1Line charge of finite length, field beside it
- Exercise 3.1.2Finite line charge, field on its own axis
- Exercise 3.1.3Two parallel line charges: the two-wire line
- Exercise 3.1.4Square loop
- Exercise 3.1.5Semicircular line charge
- Exercise 3.1.6Circular loop with a nonuniform charge
- Exercise 3.1.7Annular disk (a washer)
- Exercise 3.1.8Disk with a radially increasing charge
- Exercise 3.1.9Half disk with a nonuniform charge
- Exercise 3.1.10Quarter annulus with a nonuniform charge