Electromagnetism · 电磁学
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| 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.
答案前的判断
- 某点电势为零并不意味着该点电场强度为零。
- 你的目标：运用静电势、电场和高斯定律。
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.
阅读关系
- 电场是电势的负梯度。一个数值和一个空间变化率是不同的物理量。
- 分析电路、磁学和电磁感应。
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.
运用定义规则
- 利用对称性结合高斯定律求解。仅知道总通量无法确定曲面上每一点的场强。
- 应用麦克斯韦方程组和电磁波关系式。
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.
检查条件
- 基尔霍夫定律追踪电路中的电荷和能量。感应电动势遵循磁通量变化并带有楞次定律符号。
- 应用麦克斯韦方程组和电磁波关系式。
在均匀带电球壳内部，由对称性和高斯定律可知 E=0。其内部电势为常数，不一定为零。对于 RC 放电过程，V(t)=V₀ exp(−t/RC)，经过一个时间常数后变为 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.
应用题目格式
- 麦克斯韦方程组将电场和磁场联系起来。真空中电磁波满足 E/B=c 并携带能量。
- 应用麦克斯韦方程组和电磁波关系式。
不要利用高斯定律声称任意非对称曲面上存在均匀电场。
Which answer fits this case? · 哪个答案符合此案例？
Use electrostatic potentials, fields and Gauss’s law · 应用静电势、电场及高斯定理
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.
保持区别
- 通量 — 场的法向分量的面积分。
- potential 电势 — 单位电荷的电势能。
- 运用静电势、电场和高斯定律。
- 分析电路、磁学和电磁感应。
- 应用麦克斯韦方程组和电磁波关系式。
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.