Calculating Solid Angles for Gauss' & Ampere's Laws

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Discussion Overview

The discussion revolves around understanding solid angles and their application in the context of Gauss' Law and Ampere's Law calculations. Participants explore the concept of solid angles as a three-dimensional analog to two-dimensional angles.

Discussion Character

  • Conceptual clarification

Main Points Raised

  • One participant requests assistance in understanding solid angles in relation to Gauss' Law and Ampere's Law.
  • Another participant explains that a solid angle is the three-dimensional counterpart to ordinary angles, relating it to the surface area of the unit sphere.
  • A further contribution states that the total solid angle of a sphere is 4π, with specific solid angles for the upper half of a sphere being 2π and for a single quadrant being π.
  • A later reply indicates that the explanation provided makes sense to the original poster.

Areas of Agreement / Disagreement

Participants appear to agree on the basic definitions and measurements of solid angles, with no significant disagreements noted in the discussion.

Contextual Notes

None noted.

Who May Find This Useful

Individuals interested in the applications of solid angles in physics, particularly in relation to Gauss' Law and Ampere's Law.

retupmoc
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Can anyone help me in understanding solid angles and how to work them out in the context of Gauss' Law and Amperes Law calculations
 
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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.
 
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
 
thanks, makes sense now
 

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