Biot-Savart's law

简明释义

毕奥-萨瓦特定律

英英释义

例句

1.Engineers use Biot-Savart's law to design electromagnets in various devices.

工程师使用Biot-Savart定律来设计各种设备中的电磁铁。

2.When calculating the force on a charged particle, Biot-Savart's law plays a crucial role.

在计算带电粒子所受的力时，Biot-Savart定律起着关键作用。

3.According to Biot-Savart's law, the magnetic field generated by a current-carrying wire can be calculated using the distance from the wire.

根据Biot-Savart定律，可以通过与导线的距离计算由电流导线产生的磁场。

4.The application of Biot-Savart's law allows scientists to predict the magnetic field strength at any point in space.

应用Biot-Savart定律使科学家能够预测空间中任何点的磁场强度。

5.In physics, Biot-Savart's law is essential for understanding the behavior of magnetic fields around conductors.

在物理学中，Biot-Savart定律对于理解导体周围磁场的行为至关重要。

作文

The study of electromagnetism is a fundamental aspect of physics that helps us understand the behavior of electric charges and magnetic fields. One of the key principles in this field is known as Biot-Savart's law, which describes how currents create magnetic fields in their vicinity. This law is named after two French physicists, Jean-Baptiste Biot and Félix Savart, who formulated it in the early 19th century. Understanding Biot-Savart's law is crucial for anyone interested in electrical engineering, physics, or even applied sciences like medical imaging and telecommunications.To grasp the essence of Biot-Savart's law, we must first consider the relationship between electricity and magnetism. When an electric current flows through a conductor, it generates a magnetic field around it. The strength and direction of this magnetic field depend on several factors, including the magnitude of the current, the shape of the conductor, and the distance from the conductor. Biot-Savart's law provides a mathematical framework to quantify these relationships.The law states that the magnetic field (•B) produced at a point in space due to a small segment of current-carrying wire is directly proportional to the current (I) flowing through the wire and inversely proportional to the square of the distance (r) from the wire to the point where the magnetic field is being measured. Mathematically, it can be expressed as:•B = (μ₀/4π) * (I * dL × r̂) / r²In this equation, μ₀ is the permeability of free space, dL is the infinitesimal length of the wire segment, and r̂ is the unit vector pointing from the wire to the point of interest. The cross product indicates that the direction of the magnetic field is perpendicular to both the direction of the current and the line connecting the wire to the observation point.One of the fascinating applications of Biot-Savart's law is in the analysis of circular loops of current. For instance, if we consider a circular loop of wire carrying a steady current, we can use Biot-Savart's law to determine the magnetic field at the center of the loop. By integrating the contributions from all the infinitesimal segments of the loop, we find that the magnetic field at the center is given by:B = (μ₀ * I) / (2 * R)where R is the radius of the loop. This result illustrates how Biot-Savart's law allows us to simplify complex problems involving current-carrying conductors.In conclusion, Biot-Savart's law is a cornerstone of electromagnetic theory that provides deep insights into the interaction between electric currents and magnetic fields. Its applications extend far beyond theoretical physics, influencing technology in various domains such as electric motors, generators, and magnetic resonance imaging (MRI). By comprehending Biot-Savart's law, students and professionals alike can better appreciate the intricate dance between electricity and magnetism that underpins much of modern science and engineering.

电磁学的研究是物理学的一个基本方面，帮助我们理解电荷和磁场的行为。在这个领域中，一个关键的原则被称为Biot-Savart定律，它描述了电流如何在其附近产生磁场。这个定律以两位法国物理学家让-巴蒂斯特·比奥和费利克斯·萨瓦尔的名字命名，他们在19世纪初提出了这个定律。理解Biot-Savart定律对于任何对电气工程、物理学甚至医学成像和电信等应用科学感兴趣的人来说都是至关重要的。要领会Biot-Savart定律的本质，我们首先必须考虑电和磁之间的关系。当电流通过导体时，它在周围产生一个磁场。这个磁场的强度和方向取决于几个因素，包括电流的大小、导体的形状以及从导体到测量磁场的点的距离。Biot-Savart定律提供了一个数学框架来量化这些关系。该定律指出，由一小段带电流的导线在空间某点产生的磁场（B）与流经导线的电流（I）成正比，与导线到测量磁场的点的距离（r）的平方成反比。数学上可以表达为：B = (μ₀/4π) * (I * dL × r̂) / r²在这个方程中，μ₀是真空的磁导率，dL是导线段的无穷小长度，r̂是指向观察点的单位向量。叉乘表示磁场的方向垂直于电流的方向和连接导线与观察点的线。Biot-Savart定律的一个迷人应用是在分析圆形电流环时。例如，如果我们考虑一个携带稳定电流的圆形导线环，我们可以使用Biot-Savart定律来确定环中心的磁场。通过对环中所有无穷小段的贡献进行积分，我们发现环中心的磁场由以下公式给出：B = (μ₀ * I) / (2 * R)其中R是环的半径。这个结果说明了Biot-Savart定律如何使我们能够简化涉及带电流导体的复杂问题。总之，Biot-Savart定律是电磁理论的基石，为电流与磁场之间的相互作用提供了深刻的见解。它的应用远远超出了理论物理，影响着电动机、发电机和磁共振成像（MRI）等多个领域的技术。通过理解Biot-Savart定律，学生和专业人士可以更好地欣赏现代科学和工程中电与磁之间错综复杂的舞蹈。