# Ampere's law

Ampere's law
관련코스 전기역학
소분류 물리
선행 키워드
연관 키워드

### Integral form

$\oint_C \mathbf{B}\cdot d\mathbf{s} = \mu_0 I_{enc}$

or

$\oint_C \mathbf{H}\cdot d\mathbf{s} = I_{f,enc}$
Sign convention
Use right-hand rule for the line integral
Possible confusion
The surface can be any surface as long as the boundary coincides with C

### Differential form

$\nabla\times\mathbf{B} = \mu_0 \mathbf{J}$

or

$\nabla\times\mathbf{H} = \mathbf{J}_f$
bound currents

The total current consists of three components:

$\mathbf{J} = \mathbf{J}_f + \underbrace{\mathbf{J}_M + \mathbf{J}_P}_{\textrm{bound currents}}$

where $\mathbf{J}_M$ is due to magnetization, whereas $\mathbf{J}_P$ is due to polarization.