Electromagnetism
| English | 中文 | Pinyin |
|---|---|---|
| potential/pəˈtenʃl/ | 电势 | diàn shì |
| flux/flʌks/ | 通量 | tōng liàng |
A decision before an answer
- Zero electric potential at a point does not imply zero electric field there.
- Your goal: Use electrostatic potentials, fields and Gauss’s law.
Read the relationship
- Electric field is the negative gradient of potential. A value and a spatial change are different quantities.
- Analyse circuits, magnetism and induction.
An RC time constant has units of:
Resistance times capacitance has units of time.
Use the defining rule
- Use Gauss’s law with symmetry. A known total flux alone does not give the field at every surface point.
- Apply Maxwell equations and electromagnetic wave relationships.
For an ideal electrostatic conductor in equilibrium, its internal electric field is:
Free charges rearrange until the internal electrostatic field vanishes.
Check the conditions
- Kirchhoff’s laws track charge and energy in circuits. Induced emf follows changing magnetic flux with the Lenz-law sign.
- Apply Maxwell equations and electromagnetic wave relationships.
Inside a spherical shell with uniformly distributed charge, symmetry and Gauss’s law give E=0. Its potential is constant inside, not necessarily zero. For an RC discharge, V(t)=V₀ exp(−t/RC), and after one time constant it is V₀/e.
For R=1000 ohms and C=0.002 farads, RC=____ seconds.
Multiply 1000×0.002=2.
Apply the task format
- Maxwell equations link electric and magnetic fields. In vacuum a wave has E/B=c and carries energy.
- Apply Maxwell equations and electromagnetic wave relationships.
Do not use Gauss’s law to claim a uniform field on an arbitrary nonsymmetric surface.
Which answer fits this case?
Use electrostatic potentials, fields and Gauss’s law
A constant nonzero potential must mean a nonzero electric field.
The field depends on the gradient, which is zero for constant potential.
Keep the distinctions
- flux 通量 — The surface integral of a field’s normal component.
- potential 电势 — Potential energy per unit charge.
- Use electrostatic potentials, fields and Gauss’s law.
- Analyse circuits, magnetism and induction.
- Apply Maxwell equations and electromagnetic wave relationships.
Match each term with its precise meaning in this lesson.
Keep the distinctions stated in the teaching example.
Put this lesson’s reasoning or event sequence in order.
The order follows the stated process; check each stage before the next.