solenoidal field

简明释义

螺线管磁场

英英释义

例句

1.In theoretical physics, certain vector fields are classified as solenoidal fields (涡旋场) due to their properties under divergence operations.

在理论物理学中，某些矢量场因其在散度运算下的特性而被归类为solenoidal fields（涡旋场）。

2.The divergence theorem helps in proving that a solenoidal field (涡旋场) has specific integral properties over closed surfaces.

散度定理有助于证明solenoidal field（涡旋场）在封闭表面上的特定积分性质。

3.In fluid dynamics, the velocity field of an incompressible fluid is represented as a solenoidal field (涡旋场), ensuring that the divergence of the velocity vector is zero.

在流体动力学中，不可压缩流体的速度场被表示为一个solenoidal field（涡旋场），确保速度向量的散度为零。

4.When analyzing electromagnetic fields, it is important to identify regions where the electric field behaves like a solenoidal field (涡旋场).

在分析电磁场时，识别电场表现为solenoidal field（涡旋场）的区域是很重要的。

5.The magnetic field generated by a long straight wire can be described as a solenoidal field (涡旋场) around the wire.

由长直导线产生的磁场可以描述为导线周围的solenoidal field（涡旋场）。

作文

In the realm of physics and engineering, the concept of a solenoidal field plays a crucial role in understanding various phenomena related to electromagnetism and fluid dynamics. A solenoidal field, by definition, is a vector field that has a divergence of zero. This means that at any point in the field, the amount of 'stuff' flowing into a point is equal to the amount flowing out, indicating that there are no sources or sinks within the field. This property makes solenoidal fields particularly significant in the study of incompressible fluids and magnetic fields.To illustrate the importance of solenoidal fields, consider the example of a magnetic field generated by a current-carrying wire. The magnetic field around the wire can be described as a solenoidal field because it exhibits circular patterns around the wire, and there are no magnetic monopoles; thus, the divergence is zero. This characteristic helps engineers design efficient electrical circuits and devices, ensuring that energy is conserved and effectively utilized.Moreover, in fluid dynamics, the concept of a solenoidal field is essential when analyzing the flow of incompressible fluids. In such cases, the velocity field of the fluid can be modeled as a solenoidal field, where the continuity equation ensures that mass is conserved. This principle allows engineers and scientists to predict how fluids behave in different environments, such as in pipes, around obstacles, or within natural bodies of water.The mathematical representation of a solenoidal field often involves the use of vector calculus. For instance, if we denote a vector field by Φ, the condition for it to be solenoidal can be expressed as ∇ · Φ = 0, where ∇ is the divergence operator. This equation indicates that the divergence of the vector field is zero, confirming that it is indeed a solenoidal field. Understanding this mathematical formulation is vital for students and professionals working in fields such as fluid mechanics, electromagnetism, and applied mathematics.Furthermore, the concept of solenoidal fields extends beyond theoretical applications. In practical scenarios, engineers utilize computer simulations to model and analyze solenoidal fields in various systems. For example, computational fluid dynamics (CFD) software relies on the principles of solenoidal fields to simulate airflow over an aircraft wing, allowing designers to optimize performance and fuel efficiency.In conclusion, the significance of the solenoidal field cannot be overstated. It serves as a foundational concept in both theoretical and applied physics, enabling us to understand and manipulate the behavior of various physical systems. From the design of electrical circuits to the analysis of fluid flow, the properties of solenoidal fields provide essential insights that drive innovation and technological advancement. As we continue to explore the complexities of the physical world, the study of solenoidal fields will undoubtedly remain a vital area of research and application.

在物理和工程领域，solenoidal field的概念在理解与电磁学和流体动力学相关的各种现象中起着至关重要的作用。solenoidal field的定义是一个散度为零的矢量场。这意味着在场中的任何一点，流入该点的“物质”量等于流出该点的量，表明场内没有源或汇。这一特性使得solenoidal fields在不可压缩流体和磁场的研究中尤为重要。为了说明solenoidal fields的重要性，可以考虑一个由载流导线产生的磁场的例子。导线周围的磁场可以被描述为solenoidal field，因为它在导线周围呈现出环绕的模式，并且没有磁单极子；因此，散度为零。这一特性帮助工程师设计高效的电路和设备，确保能量得以保存和有效利用。此外，在流体动力学中，solenoidal field的概念在分析不可压缩流体的流动时至关重要。在这种情况下，流体的速度场可以建模为solenoidal field，其中连续性方程确保质量得到保护。这个原理使工程师和科学家能够预测流体在不同环境中的行为，例如在管道中、障碍物周围或自然水体内。solenoidal field的数学表示通常涉及向量微积分的使用。例如，如果我们用Φ表示一个矢量场，那么它成为solenoidal的条件可以表示为∇ · Φ = 0，其中∇是散度算子。这个方程表明矢量场的散度为零，确认它确实是solenoidal field。理解这一数学表述对在流体力学、电磁学和应用数学等领域工作的学生和专业人士至关重要。此外，solenoidal fields的概念超越了理论应用。在实际场景中，工程师利用计算机模拟来建模和分析各种系统中的solenoidal fields。例如，计算流体动力学（CFD）软件依赖于solenoidal fields的原理来模拟空气流过飞机机翼的情况，使设计者能够优化性能和燃油效率。总之，solenoidal field的重要性不容小觑。它作为理论和应用物理的基础概念，使我们能够理解和操控各种物理系统的行为。从电路设计到流体流动分析，solenoidal fields的特性提供了推动创新和技术进步的重要见解。随着我们继续探索物理世界的复杂性，solenoidal fields的研究无疑将继续成为一个重要的研究和应用领域。