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# 物理代写|电磁学代写Electromagnetism代考|Magnetic Field Intensity

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## 物理代写|电磁学代写Electromagnetism代考|Magnetic Field Intensity

Figure 4.13 illustrates four air regions all of which are taken to be currentfree. Therefore, for each region the curl of magnetic field intensity is zero. Its divergence is also zero, that is,
$$\begin{gathered} \nabla \times \boldsymbol{H}=0 \ \nabla \cdot \boldsymbol{H}=0 \end{gathered}$$
Since
$$\nabla \times \nabla \times H \equiv \nabla(\nabla \cdot H)-\nabla^2 H$$
It gives
$$\nabla^2 H=0$$
The magnetic field intensity in each of the four regions satisfies Equations 4.110a through 4.111. Also, all the components of magnetic field intensity in these regions satisfy the Laplace equation. The tangential components of magnetic field on iron surfaces may thus be neglected. Further, the magnetic field vanishes at far distances from its source, that is, the current-sheet simulating the end-winding located at $z=0$. In view of the above specified conditions, the field distributions in different regions can thus be obtained.

## 物理代写|电磁学代写Electromagnetism代考|Field in Region 1

The field distribution in region 1 can be written by setting,
$$\alpha_{m, p}=\sqrt{\left(\frac{m \pi}{\lambda}\right)^2+\left(\frac{p \pi}{d}\right)^2}$$
We can write the expressions to represent field components as
\begin{aligned} H_{1 x} & =\sum_{p=1}^{\infty} P_{m, p}^{\prime}\left(\frac{p \pi}{d}\right) \cdot \cos \left(\frac{p \pi}{d} \cdot x\right) \cdot e^{-\left(\alpha_{m, p} \cdot z\right)} \ H_{1 y} & =\sum_{p=1}^{\infty} P_{m, p}^{\prime} \cdot\left(j \frac{m \pi}{\lambda}\right) \cdot \sin \left(\frac{p \pi}{d} \cdot x\right) \cdot e^{-\left(\alpha_{m, p} \cdot z\right)} \end{aligned}

$$H_{1 z}=-\sum_{p=1}^{\infty} P_{m, p}^{\prime} \cdot \alpha_{m, p} \cdot \sin \left(\frac{p \pi}{d} \cdot x\right) \cdot e^{-\left(\alpha_{m, p} \cdot z\right)}$$
where $P_{m, p}^{\prime}$ indicates a set of arbitrary constants.
4.6.2.2 Field in Region 2
The distribution of magnetic field intensity in region 2 can be given as
\begin{aligned} H_{2 x} & =\sum_{p=1}^{\infty} P_{m, p}^{\prime \prime} \cdot\left(\frac{p \pi}{d}\right) \cdot \cos \left(\frac{p \pi}{d} \cdot x\right) \cdot e^{\alpha_{m, p} \cdot(z+g)} \ H_{2 y} & =\sum_{p=1}^{\infty} P_{m, p}^{\prime \prime} \cdot\left(j \frac{m \pi}{\lambda}\right) \cdot \sin \left(\frac{p \pi}{d} \cdot x\right) \cdot e^{\alpha_{m, p} \cdot(z+g)} \ H_{2 z} & =\sum_{p=1}^{\infty} P_{m, p}^{\prime \prime} \cdot \alpha_{m, p} \cdot \sin \left(\frac{p \pi}{d} \cdot x\right) \cdot e^{\alpha_{m, p} \cdot(z+g)} \end{aligned}
where $P_{m, p}^{\prime \prime}$ indicates a set of arbitrary constants.

where, $a_m$ and $b_{m, q}$ indicate two sets of arbitrary constants. The first terms on the right-hand side of Equations 4.114a and $4.114 \mathrm{c}$ indicate field components due to the current-sheet simulating the main winding housed in the stator slots. The remaining terms in these field equations vanish deep inside the air gap, far removed from the end-winding, that is, as $x \rightarrow-\infty$.
Therefore, as $x \rightarrow-\infty,\left.H_{3 z}\right|_{z=0}=a_m=k_m$.

## 物理代写|电磁学代写Electromagnetism代考|Magnetic Field Intensity

$$\begin{gathered} \nabla \times \boldsymbol{H}=0 \ \nabla \cdot \boldsymbol{H}=0 \end{gathered}$$

$$\nabla \times \nabla \times H \equiv \nabla(\nabla \cdot H)-\nabla^2 H$$

$$\nabla^2 H=0$$

## 物理代写|电磁学代写Electromagnetism代考|Field in Region 1

$$\alpha_{m, p}=\sqrt{\left(\frac{m \pi}{\lambda}\right)^2+\left(\frac{p \pi}{d}\right)^2}$$

\begin{aligned} H_{1 x} & =\sum_{p=1}^{\infty} P_{m, p}^{\prime}\left(\frac{p \pi}{d}\right) \cdot \cos \left(\frac{p \pi}{d} \cdot x\right) \cdot e^{-\left(\alpha_{m, p} \cdot z\right)} \ H_{1 y} & =\sum_{p=1}^{\infty} P_{m, p}^{\prime} \cdot\left(j \frac{m \pi}{\lambda}\right) \cdot \sin \left(\frac{p \pi}{d} \cdot x\right) \cdot e^{-\left(\alpha_{m, p} \cdot z\right)} \end{aligned}

$$H_{1 z}=-\sum_{p=1}^{\infty} P_{m, p}^{\prime} \cdot \alpha_{m, p} \cdot \sin \left(\frac{p \pi}{d} \cdot x\right) \cdot e^{-\left(\alpha_{m, p} \cdot z\right)}$$

4.6.2.2区域2中的字段说明

\begin{aligned} H_{2 x} & =\sum_{p=1}^{\infty} P_{m, p}^{\prime \prime} \cdot\left(\frac{p \pi}{d}\right) \cdot \cos \left(\frac{p \pi}{d} \cdot x\right) \cdot e^{\alpha_{m, p} \cdot(z+g)} \ H_{2 y} & =\sum_{p=1}^{\infty} P_{m, p}^{\prime \prime} \cdot\left(j \frac{m \pi}{\lambda}\right) \cdot \sin \left(\frac{p \pi}{d} \cdot x\right) \cdot e^{\alpha_{m, p} \cdot(z+g)} \ H_{2 z} & =\sum_{p=1}^{\infty} P_{m, p}^{\prime \prime} \cdot \alpha_{m, p} \cdot \sin \left(\frac{p \pi}{d} \cdot x\right) \cdot e^{\alpha_{m, p} \cdot(z+g)} \end{aligned}

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