Why Are the Integration Limits for Spherical Coordinates 0 to Pi and 0 to 2Pi?

[bcjochim07]

Homework Statement

I am reading through my textbook about an application of the divergence theorem involving a point charge enclosed by some arbitrary Gaussian surface. When the author evaluates the ∫_sE dot dA, they rewrite the expression as a double integral in spherical coordinates I am fine with this except I can't quite grasp the limits of integration that are given; they are 0 to pi and 0 to 2pi. I am having trouble picturing how these rotations integrate over the whole sphere, as I keep visualizing that both the limits should be 0 2pi. Any suggestions would be greatly appreciated. Thanks.

Homework Equations

The Attempt at a Solution

 

[lanedance]

that would cover the surface twice

2 pi is one full revolution

imagine half a circle, swept by a line rotated at its base from 0 to pi

then rotate this about the axis defining by the half circle by full 2 pi to generate a sphere

http://mathworld.wolfram.com/SphericalCoordinates.html

 

[lanedance]

that would cover the surface twice

2 pi is one full revolution

imagine half a circle, swept by a line rotated at its base from 0 to pi

then rotate this about the axis defining by the half circle by full 2 pi to generate a sphere

http://mathworld.wolfram.com/SphericalCoordinates.html