It's fairly detailed. You will need to indicate where you think some steps have been missed.cwill53 said:
Taking a look at it again, I believe my issues can be chalked up to vector calculus weakness. I'm trying to work through it all, it will just take time. I will ask again if I'm still confused after I strengthen my calculus.haruspex said:
The solid angle is a measure of the amount of space an object occupies in three-dimensional space. It is used in Gauss' Law to simplify the calculation of electric flux, which is the amount of electric field passing through a given surface.
By using the solid angle, the integral in Gauss' Law can be simplified to a single variable, making it easier to solve. This is because the solid angle takes into account the angle at which the electric field lines pass through the surface, reducing the need for complex trigonometric calculations.
Yes, the solid angle can be used for any shape or surface, as long as the electric field lines are passing through it. It is a universal concept that can be applied to any situation where Gauss' Law is applicable.
No, the use of solid angle is not necessary for deriving Gauss' Law. It is simply a mathematical tool that can make the calculation process easier and more efficient.
While the use of solid angle can simplify the integral in Gauss' Law, it may not always be the most efficient method. In some cases, it may be easier to use other techniques such as symmetry or vector calculus to solve the problem. Additionally, the solid angle may not be applicable in situations where the electric field lines are not passing through the surface at a constant angle.