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

Gravitational, Electric and Magnetic Fields

How does dividing force by a test mass or test charge turn gravity and Coulomb's law into fields?

Loading…

←Previous Curl: Measuring the Circulation of a Field Next Drawing Vector Fields: Arrows, Lines and Grass Seeds →

Your summary note

1. Gravitational field $\vec{g}=-\frac{GM}{r^2}\hat{r}$
  Derive $\vec{g}$ as the limit of $\vec{F}_g/m$ from Newton's law, state its inward radial direction, and compute $g=GM/R_E^2\approx 9.8\ \text{m/s}^2$ for the uniform field near the surface.
2. Electric field $\vec{E}=k_e\frac{Q}{r^2}\hat{r}$ of a point charge
  Define $\vec{E}$ as the limit of $\vec{F}_e/q$ for a test charge, give its unit N/C, record outward for positive $Q$ and inward for negative $Q$ , and write $\vec{F}_e=q\vec{E}$ .
3. Sources of magnetic fields and their directions
  Record that like poles repel, compass needles align with $\vec{B}$ , moving charges create $\vec{B}$ , Earth's magnetic south pole lies in the north, and sketch a wire's circular field by the right-hand rule.
Attempt 1 of 2