Calculating Solid Angles for Gauss' & Ampere's Laws

[retupmoc]

Can anyone help me in understanding solid angles and how to work them out in the context of Gauss' Law and Amperes Law calculations

 

[Tide]

A solid angle is the 3-dimensional analog of angles in two dimensions. Ordinary angles refer to a portion of full rotation in a plane corresponding to the circumference of the unit circle. An angle is the circumference of the unit circle subtended by the rotation. Think of it as having one degree of freedom.

In three dimensions, rotations have two degrees of freedom and the appropriate measure for rotation corresponds to the surface area of the unit circle.

 

[HallsofIvy]

Since the surface area of the unit sphere is 4π, we take the measure of a "whole solid angle" to be 4π and then measure other solid angles as fractions of that.

The solid angle corresponding to a the upper half of a sphere is 2π

The solid angle corresponding to a single quadrant is π

 

[retupmoc]

thanks, makes sense now