物理代写|几何光学代写Geometrical Optics代考|OPTI502

2023年1月2日

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物理代写|几何光学代写Geometrical Optics代考|Magnetic Field

The magnetic field is usually represented by symbol $\mathbf{B}$. To determine the direction of the magnetic field $\mathbf{B}$ at some location the compass needle is used, which points along B at that location. The magnetic field lines outside a magnet go from north poles to south poles, as shown in Fig. 6.1. It is common to use small iron filings to display magnetic field line patterns of a bar magnet. To define the magnetic field $\mathbf{B}$ at any location in space, the magnetic force $\mathbf{F}_B$ that the field exerts on a test object can be used. For that, we can use a charged particle moving with some velocity of v. Furthermore, we ignore the presence of the gravitational field or an electric field at the position of the test object.

Mathematically, those observations can be formulated in the following form:
$$\mathbf{F}B=q \mathbf{v} \times \mathbf{B}$$ Equation (6.1) indicates that the direction of $\mathbf{F}_B$ applied on a positive charge particle $q$ is in the direction of $\mathbf{v} \times \mathbf{B}$, and hence, by definition of the cross product, it is perpendicular to both $\mathbf{v}$ and $\mathbf{B}$ (see Fig. 6.3). Furthermore, if $q$ is a negative charge, then $\mathbf{F}_B$ is opposite to the direction of $\mathbf{v} \times \mathbf{B}$. Moreover, Eq. (6.1) implies that the magnitude of the magnetic force $F_B$ is $$F_B=|q| v B \sin \theta$$ Here, $\theta$ is the smaller angle between $\mathbf{v}$ and $\mathbf{B}$. Equation (6.2) implies that $F_B=0$ if $\mathbf{v}$ is parallel or antiparallel to $\mathbf{B}$ (that is, $\theta=0$ or $\left.180^{\circ}\right)$ and maximum $\left(F{B, \max }=q v B\right.$ ) if $\mathbf{v}$ is perpendicular to $\mathbf{B}$ (that is, $\theta=90^{\circ}$ ). Equation (6.2) defines the operational function of the magnetic field $\mathbf{B}$ at some point in space; that is, if a moving charged particle is placed at that location in space, the magnetic field is defined in terms of the force acting on that charge.

物理代写|几何光学代写Geometrical Optics代考|Magnetic Force Acting on a Current-Carrying

Consider the magnetic force exerted on a single charged particle that moves through a magnetic field given by Eq. (6.1). If we suppose having a conducting wire in which a current is maintained, for example, by utilizing a battery, then it should experience a force when placed in a magnetic field. That is because the current is a stream of mobile charged particles. Thus, the net force acting by the field on the wire is the directorial sum of the individual forces exerted on all the charged particles making up that current. When the mobile charged particles collide with atoms of the conducting wire, then those magnetic forces used on the charged particles transmit to the wire.
We will consider a straight segment of wire with length $L$ and cross-sectional area $A$, carrying a steady current $I$, to quantify the magnetic force applied by the magnetic force on a current-carrying wire. Furthermore, suppose that the wire is placed in a uniform magnetic field $\mathbf{B}$, as shown in Fig. 6.4. The magnetic force exerted on a charge $q$ moving with a drift velocity $\mathbf{v}_d$ is given by Eq. (6.1) as $$\mathbf{f}_B=q \mathbf{v}_d \times \mathbf{B}$$
We denote by $N_q$ the total number of charges in that segment, given as: $N_q=n A L$, where $n$ is the number of charges per unit volume and $A L$ gives the volume of the segment. Then, to find the total force exerted on the wire, we multiply the force $\mathbf{f}_B$ exerted on one charge by $N_q$. Hence, the total magnetic force on the wire of length $L$ is
$$\mathbf{F}_B=N_q \mathbf{f}_B=n A L q \mathbf{v}_d \times \mathbf{B}$$
Since the current is $I=n q v_d A$, then
$$\mathbf{F}_B=I(\mathbf{L} \times \mathbf{B})$$
In Eq. (6.8), $\mathbf{L}$ is a vector pointing in the same direction as the current $I$ and has a magnitude equal to the length $L$ of the segment.

几何光学代考

物理代写|几何光学代写Geometrical Optics代考|Magnetic Field

$$\mathbf{F} B=q \mathbf{v} \times \mathbf{B}$$

$$F_B=|q| v B \sin \theta$$

物理代写|几何光学代写Geometrical Optics代考|Magnetic Force Acting on a Current-Carrying

$$\mathbf{f}_B=q \mathbf{v}_d \times \mathbf{B}$$

$$\mathbf{F}_B=N_q \mathbf{f}_B=n A L q \mathbf{v}_d \times \mathbf{B}$$

$$\mathbf{F}_B=I(\mathbf{L} \times \mathbf{B})$$

有限元方法代写

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MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。