Induced Electric Field

Core Sentence / 核心句

A changing magnetic flux creates a circulating, non-conservative electric field.

中文理解：变化磁通量在空间中建立环形感生电场；wire 不是产生该场的必要条件，只是给 free charges 提供运动路径。

\oint_{C} E \cdot d ℓ = - \frac{d Φ _{B}}{d t}

differential form：

\nabla \times E = - \frac{\partial B}{\partial t}

Electrostatic field	Induced electric field
produced by stationary charge distribution	produced by changing magnetic field
conservative	non-conservative
$\oint E \cdot d ℓ = 0$	$\oint E \cdot d ℓ \neq = 0$ when flux changes
globally described by scalar potential in a simply connected region	cannot generally be described by one single-valued electrostatic potential
field lines begin/end on charge	field lines can form closed loops

The wire reveals the induced field; it does not create the field.

导线让感生电场表现为电流，但不是导线创造了感生电场。

nonzero closed-loop integral means non-conservative；
do not apply “potential always decreases along the field” around an induced-field closed loop；
Faraday’s law uses a closed path and magnetic flux through a spanning surface；
Gauss’s law uses a closed surface and enclosed charge。