EM · Electromagnetism

GRE · GRE Subject Test · GRE 物理 · 知识点 2

2.1

电磁学

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

English	中文	拼音
potential/pəˈtenʃl/	电势	diàn shì

2.2

Choose the system and model

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

2.3

Use the governing relation

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

词汇训练

English	中文	拼音
flux/flʌks/	通量	tōng liàng

2.4

Apply the conditions

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

2.5

Check the conclusion

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

2.6

Worked method

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.

$$4\pi r^2E=Q/\epsilon_0,\qquad E=Q/(4\pi\epsilon_0r^2)\quad(r>R).$$

Inside, enclosed charge is zero and symmetry gives E = 0. Continuity gives

$$V(r)=\begin{cases}Q/(4\pi\epsilon_0R)&r;\leq R,\\Q/(4\pi\epsilon_0r)&r;>R.\end{cases}$$

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.