Chapter 1 — Electric Charges and Fields
Two kinds of charge, one inverse-square force, and the idea of a field that fills space — the foundation for all of electricity and magnetism.
A thundercloud over Mumbai in the monsoon separates charge on a vast scale: colliding ice crystals and soft hail leave the top of the cloud positive and the bottom negative, and a single lightning flash can carry a few tens of coulombs to the ground in a fraction of a second. Your phone's touchscreen does something far gentler: it senses the tiny change in charge on a grid of transparent electrodes when your finger comes near. Inkjet printers steer charged droplets, factories coat car bodies with charged paint spray, and power stations clean their smoke with charged plates that pull ash out of the gas. All of these rest on the physics of charges at rest — electrostatics.
This chapter answers three questions. What is electric charge, and how does it behave? How hard do two charges push or pull on each other (Coulomb's law), and how do many charges combine (superposition)? And how can we describe the influence of charges on the space around them, so that we can say what force any charge would feel at any point? The answer to the last question — the electric field — leads to field lines, electric dipoles, the flux of a field through a surface and finally Gauss's law, a short equation that turns hard superposition sums into one-line calculations whenever there is symmetry.
- use additivity, conservation and quantisation of charge, and explain charging by friction, conduction and induction;
- calculate Coulomb forces in vacuum and in a medium, and add the forces from several charges as vectors;
- find the electric field of point charges and of a dipole (on its axis and equatorial line), sketch field lines, and find the torque on a dipole in a uniform field;
- calculate electric flux and use Gauss's law to find the field of an infinite line charge, an infinite plane sheet and a thin spherical shell;
- solve board, JEE Main, JEE Advanced and NEET problems on all of the above.
Sections in this chapter
Electric Charge, Conductors and Coulomb's Law
Two kinds of charge, conservation and quantisation, conductors and induction, the inverse-square law and superposition of forces.
The Electric Field, Field Lines and Electric Dipoles
Force per unit charge, fields of point charges, field lines, the dipole field and the torque on a dipole.
Electric Flux, Gauss's Law and Its Applications
Continuous charge distributions, flux through a surface, Gauss's law and fields of lines, sheets and shells.