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

Electric Pressure and Tension: The Stress ε₀E²/2

Why do field lines pull along their length and push sideways, both with stress ε₀E²/2?

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Your summary note

1. Force on a charge held in a growing external field
  Set the charge's own field equal to $E_0$ to find $r_0$ , multiply the stress $\frac{\varepsilon_0 E_0^2}{2}$ by the area $4\pi r_0^2$ , and show the result is of order $qE_0$ .
2. Like and unlike charges on pendulums
  Describe the field-line pictures for like and unlike charges, and record that pressure perpendicular to the field pushes like charges apart while tension along the field pulls unlike charges together.
3. Tension and pressure on the faces of a box
  Sketch a box in a uniform vertical field, mark the pull on top and bottom and the push on the sides, show they cancel, then redo it with the bottom inside a capacitor plate.
4. Common magnitude $\frac{\varepsilon_0 E^2}{2}$ and energy density
  Record the definitions of tension (stress along the outward normal) and pressure (stress perpendicular to it), state their common magnitude $\frac{\varepsilon_0 E^2}{2}$ , and check its units are those of pressure and of energy density.
Attempt 1 of 2