Solid angle or steradian for measuring

In summary, solid angles or steradians are used for measuring in cases where Gauss's law for closed surfaces needs to be proven. They are also useful for measuring radiant intensity and in geometric phase problems. In contrast to normal angles, solid angles are more general and can be applied to different shapes in higher dimensions. They are also important in experimental particle scattering. In mathematics, solid angles are not commonly used for solving problems involving cones and spheres.
  • #1
monty37
225
1
where do we use solid angle or steradian for measuring,in what way
is theuseful over normal angle?
 
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  • #2


They are useful for proving the generality of Gauss's law for closed surfaces.
 
  • #3


Consider a sphere and a cone emanating from the center, now how do you apply "normal" angles to describe the cone?
 
  • #4


They are also useful in the measure of radiant intensity.
 
  • #5


Geometric phase problems sometimes has them, like with Foucalt's pendulum.
 
  • #6


They are very useful, of course, if you review the definition of Radian, you'll find the it's the angle where the length of the arc is equal to the radius, in different angles, you'll be taking the ratio between the arc and the radius.
In 3D case, you'll find yourself talking about an area and a cone, this cone doesn't necessarily have to be based on a circle, maybe on some elliptical shape, this gives some kind of a generalisation to the definition of an angle in higher dimensions, that it's a ratio, more than being a physical quantity.

If I'm not right, I'd love someone to correct for me :)

Good luck :)
 
  • #7


Prove that the surface area of a sphere of radius R is 4 pi R2. The 4 pi steradians is the solid angle of the entire surface.
 
  • #8


monty37 said:
where do we use solid angle or steradian for measuring,in what way
is theuseful over normal angle?

They're also important in experimental particle scattering where one theoretically calculates the solid body angle.
 
  • #9


why is it that solid angles are not used while dealing with three dimensional geometry,in mathematics,there all the problems involving cones and spheres were done using normal
angles.
 

1. What is solid angle and how is it different from regular angle?

Solid angle is a measure of the amount of space covered by a three-dimensional object as viewed from a specific point. It is different from regular angle, which is a measure of the amount of rotation required to move from one line to another. Solid angle is measured in steradians (sr), while regular angle is measured in degrees or radians.

2. How is solid angle related to the area of a surface?

Solid angle is directly proportional to the surface area of an object. This means that as the surface area increases, the solid angle also increases. This relationship is expressed mathematically as Ω = A/r², where Ω is the solid angle, A is the surface area, and r is the distance from the viewing point to the object.

3. Why is solid angle used instead of regular angle for measuring three-dimensional objects?

Solid angle is used for measuring three-dimensional objects because it takes into account the curvature of the surface. Regular angle is only applicable to flat surfaces, while solid angle can be used for any three-dimensional object, regardless of its shape or orientation.

4. How is solid angle measured?

Solid angle is measured in steradians (sr), which is equal to the area of a unit sphere (4π) divided by the square of the radius. It can also be calculated by dividing the surface area of an object by the square of the distance from the viewing point to the object.

5. What are some real-world applications of solid angle?

Solid angle has many applications in fields such as astronomy, physics, and engineering. It is used to measure the amount of light emitted by a light source, calculate the intensity of radiation from a nuclear source, and determine the field of view of a camera or telescope. It is also used in the design of solar panels, satellite communication systems, and virtual reality technology.

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