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

01Charge Density and the Field on a Rod's Axis 02The Field on a Charged Rod's Perpendicular Bisector 03The Fields of a Charged Ring and a Charged Disk 04How Field Lines Carry Force, Energy and Momentum 05Electric Pressure and Tension: The Stress ε₀E²/2 Problem set0/10 Problem set 20/10 MIT problem set0/6

How Field Lines Carry Force, Energy and Momentum

If there is no action at a distance, how do field lines carry force, energy and momentum between charges?

Loading…

←Previous The Fields of a Charged Ring and a Charged Disk Next Electric Pressure and Tension: The Stress ε₀E²/2 →

Your summary note

1. Repulsion and attraction near a van de Graaff sphere
  Sketch the total field lines for a small sphere carrying like and then unlike charge, and state that the force passes through the field at the speed of light, not by action at a distance.
2. Tension and pressure giving the force $q\vec{E}$
  Draw the charge at rest at the origin in $\vec{E} = -E_0\hat{\mathbf{k}}$ with an imaginary sphere around it, mark where the lines pull and where they push, and show both give $-qE_0\hat{\mathbf{k}}$ .
3. Energy and momentum exchanged with the field
  Trace the charge rising, stopping and falling back, record where its kinetic energy goes as it slows and where it comes from as it speeds up, and state which objects receive its $z$ -momentum.
Attempt 1 of 2