Spherical polar co-ordinate:
The spherical polar co-ordinate system is a method of representation, which helps to represent the co-ordinates of a point on the surface of a sphere. There are three co-ordinates in this system.
The three co-ordinates for a point A in the spherical polar co-ordinate system are given bellow:
- The radial distance of point A from the origin O of the spherical co-ordinate system is \( \vec{OA}=\vec{r} \). The vertical plane with contains \( \vec{r} \) is known as the azimuthal plane.
- The radius vector \( \vec{r} \) makes an angle \( \theta \) with the vertical positive Z-axis. Angle \( \theta \) is known as the co-latitude angle or zenith angle.
- The azimuthal plane makes an angle \( \phi \) with the ZX-plane. This angle \( \phi \) is known as the azimuthal angle. In the figure, the azimuthal angle \( \phi \) is made by the line OB with the positive X-axis OX.
Limits of the co-ordinates :
- Limit of \( \vec{r} \): The value of r is always positive. It can take any value from 0 to infinity.
- Limit of \( \theta \): The co-latitude angle or zenith angle \( \theta \) always lies between zero to \( \pi \).
- Limit of \( \phi \): The azimuthal angle \( \phi \) lies between 0 to \( 2\pi \).