Understanding Length and Area Elements for Electromagnetic Laws

In summary, the conversation discusses the difficulty in finding length and area elements for Gauss's, Ampere's, and Biot-Savart Laws. The speaker asks for help in understanding this concept for symmetrical, non-symmetrical, and infinite objects. They also mention the use of an infinitesimal distance called ds and how to determine its value. Another person clarifies that ds is a differential and cannot be given a numerical value, but rather is used in integration.
  • #1
tblount2
1
0
I'm having a difficult time figuring out how to find length and area elements for Gauss's, Ampere's, and Biot-Savart Laws! Can someone please help explain! This applies to symmetrical, non-symmetrical, and infinite objects! I'm not asking what is the area of a sphere but, say with an infinite object, you use a small portion maybe called ds, well how do you figure how what your value of ds will be? And please don't give an example using a simple figure! That won't help me! I've noticed that if I understand the most difficult then I'm good to go for everything! Thanks :)
 
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  • #2
ds is an infinitesimal distance which u can chose in cartesian coordinates, cylindrical or spherical coordinates. U want to chose ds along the line which contains the flux or the current, ...
 
  • #3
You don't "figure out your value of ds". A differential has no value in terms of numbers. You integrate with respect to s.
 

1. What is the difference between length and area elements?

Length elements refer to one-dimensional measurements, such as the distance between two points or the length of a line. Area elements, on the other hand, refer to two-dimensional measurements, such as the size of a surface or the area of a shape.

2. How are length and area elements measured?

Length elements are usually measured using units such as meters (m) or inches (in). Area elements are measured using units squared, such as square meters (m2) or square inches (in2).

3. What is the significance of length and area elements in science?

Length and area elements are important in science because they allow us to accurately measure and describe the physical world around us. They are used in various fields of science, including physics, engineering, and biology.

4. Can length and area elements be converted into each other?

Yes, length and area elements can be converted into each other using mathematical formulas. For example, to convert from meters to square meters, you would multiply the length in meters by itself (m x m = m2). Similarly, to convert from square inches to square feet, you would divide the area in square inches by 144 (in2 / 144 = ft2).

5. How do length and area elements relate to volume?

Length and area elements are important in determining volume, which is a three-dimensional measurement. To calculate volume, you would multiply the length, width, and height (all measured in length elements) together. For example, the volume of a cube with sides measuring 5 inches would be 5 x 5 x 5 = 125 in3.

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