What is the PHI coordinate of the point present on Z-axis?

We start studying Electromagnetics with Coordinate Systems. Cylindrical Coordinate System and Spherical Coordinate System possess phi coordinate. Let’s see what value of phi you should take for the points on the Z-axis.

Cylindrical Coordinate System

In cylindrical coordinate system, any point in the space is represented by three coordinates viz. rho, phi and z.

Rho coordinate is the lateral distance of the given point from Z-axis.

Phi coordinate is the angle made by the vertical half plane (containing the point) with +X axis.

Now, the range of phi coordinate can be anywhere between 0 to 360^o (2π) to cover the entire space.

Point on Z-axis

Now, for any point that is present on the Z-axis will be contained by any vertical half plane, isn’t it?

What actually is the vertical half plane? It is the semiinfinite half plane attached to the Z axis. And, as point itsself present on the Z axis, any vertical half plane will be valid for it.

In other words, any value of phi would be justified for such point.

So, the point present on Z axis can have any value between 0 to 360^o (2π).

Pro Tip

Though you can take any anle as the phi coordinate, for a point present on the Z axis; you should take phi of such point equal to the phi of other point which is related to it. This will surely reduce your calculations.

Simple!