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likephysics
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Homework Statement
This is not a HW prob. Just a question.
When doing surface integrals, why should the area element ds be dotted with the normal. I don't get it .
[tex]\oint[/tex]A.n ds
likephysics said:Homework Statement
This is not a HW prob. Just a question.
When doing surface integrals, why should the area element ds be dotted with the normal. I don't get it .
[tex]\oint[/tex]A.n ds
A surface integral is a type of mathematical calculation used to find the total value of a function over a given surface. It involves integrating the product of the function and a differential element that represents the surface area, such as dot ds with normal.
The dot ds with normal is a crucial component in surface integrals because it helps to determine the orientation of the surface. This information is necessary for accurately calculating the surface integral.
Dot ds with normal is calculated by taking the dot product of two vectors: the unit vector normal to the surface (ds) and the differential element representing the surface area (ds). This calculation gives the magnitude of the surface element in a specific direction.
The main difference between surface integrals and line integrals is the shape of the integration path. In surface integrals, the path is a two-dimensional surface, while in line integrals, the path is a one-dimensional curve.
Surface integrals are used in various fields of science, such as physics, engineering, and mathematics, to calculate physical quantities, such as flux, electric potential, and work done. They are also used to solve problems involving surfaces, such as finding the center of mass or determining the surface area of a three-dimensional object.