EM · Electromagnetism

Zero electric potential 电势 at a point does not imply zero electric field there.

Prerequisites: 13, 14, 15, 29, 30.

• Use electrostatic potentials, fields and Gauss’s law
• Analyse circuits, magnetism and induction
• Apply Maxwell equations and electromagnetic wave relationships

Electric field is the negative gradient of potential. A value and a spatial change are different quantities.

Use Gauss’s law with symmetry. A known total flux 通量 alone does not give the field at every surface point.

Kirchhoff’s laws track charge and energy in circuits. Induced emf follows changing magnetic flux with the Lenz-law sign.

Maxwell equations link electric and magnetic fields. In vacuum a wave has E/B=c and carries energy.

A spherical shell has radius R and uniform charge Q. Choose zero potential at infinity. Spherical symmetry lets Gauss's law 高斯定律 determine the field outside.

Inside, enclosed charge is zero and symmetry gives E = 0. Continuity gives The potential is nonzero and constant inside. A zero gradient, rather than a zero value, gives a zero field. The radial field jumps at the charged surface.

Do not use Gauss’s law to claim a uniform field on an arbitrary nonsymmetric surface.

flux: The surface integral of a field’s normal component.

potential: Potential energy per unit charge.