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:

1. 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.
2. 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.
3. 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  \( 2\pi \).