# Maxwell静磁均匀磁场

### 二维下的推导

Vector Potential实际上就是磁矢位$$A_z$$，根据$$\boldsymbol{B}=\triangledown\times\boldsymbol{A}$$，对于二维问题，$$A_x=0$$，$$A_y=0$$有

$B_x=\frac{\mathrm{d} A_z}{\mathrm{d} y}$

$B_y=-\frac{\mathrm{d} A_z}{\mathrm{d} x}$

### Maxwell中对边界的解释

Zero Tangential H Field: Flux is perpendicular if tangent components are zero or if a zero tangential H-field boundary condition was applied. 切向分量为零，磁通垂直于指定面。

Tangential H Field: The tangential components of H are set to pre-defined values. 切向分量被指定为预设值，可通过U（X）和V（Y）分量的组合实现。

Integrated Zero Tangential H Field: For applications such as a motor with the shaft excluded, there remains a hole in the middle. In such cases, on the hole’s boundary, neither the Tangential H Field boundary, nor the Zero Tangential H Field boundary can be applied because – for the hole boundary case – integration of the tangential H field is zero, but the tangential H field is not zero everywhere. Integrated Zero Tangential H Field can be used for such applications. 切向H并不出处为零，但在该面上的积分为零。

### Maxwell的默认边界

These boundary conditions are automatically defined for a magnetostatic model:

• Natural boundaries are assigned to the surfaces between objects. 物体之间的表面被赋予了自然边界。
• Neumann boundaries are assigned to the outside edges of the problem region. 诺依曼边界被分配到问题区域的外部边缘。

To leave a surface set to its default boundary condition, do nothing. Deleted boundary conditions and excitations automatically reset to the default boundary conditions. 若要将曲面设置为默认边界条件，则不执行任何操作。删除的边界条件和激励自动重置为默认边界条件。

• 第一类边值条件：也称为狄利克雷边界条件，直接描述物理系统边界上的物理量，例如振动的弦两端与平衡位置的距离；
• 第二类边值条件：也称为诺伊曼边界条件，描述物理系统边界上物理量垂直边界的导数的情况，例如导热细杆端点的热流；
• 第三类边值条件：物理系统边界上物理量与垂直边界导数的线性组合，例如，细杆端点的自由冷却，温度、热流均不确定，但是二者的关系确定，即可列出二者线性组合而成的边值条件。

Maxwell中的默认诺依曼条件为齐次，即法向导数为零。