what is the cylindrical coordinate system?

what is the cylindrical coordinate system?

what is the cylindrical coordinate system? This system helps to analyze the geometry of a coaxial cable and we can analyze its  electric field intensity or electric field more easily using them. Three coordinates that are used for representing a point in cylindrical are P(р,Ф,Ζ). р is the radial distance of a cylindrical surface, Ф is the angle that a point makes with the x-axis in counter clockwise direction, z is the height of a cylinder. These three coordinates give us constant planes. At top surface of the cylinder, z is constant while  р andФ are variables. Similarly at outer cylindrical surface, р is constant while Ф and Ζ are variable. The cross sectional plane obtained by cutting the cylinder vertically gives us a plane on which Ф is constant while р and Ζ vary.

The following picture shows how these cylindrical coordinate systems with their unit vectors are represented.

cylindrical coordinate system
cylindrical coordinate system

1. **ρ (rho)**: As in the standard cylindrical system, ρ represents the radial distance from the origin to a point in space. In electrical engineering, this coordinate is used to specify distances from the central axis of a cylindrical structure, such as a wire or a coaxial cable.

2. **θ (theta)**: Theta still represents the angle measured counterclockwise from the positive x-axis to the projection of the point in the xy-plane. In electrical engineering, this angle helps determine the orientation of electric or magnetic fields around cylindrical structures.

3. **z (z)**: The z-coordinate remains the same, representing the height or distance along the central axis of the cylindrical structure.

Cylindrical coordinates in electrical engineering are particularly useful for solving problems related to:

– **Electrostatics**: Analyzing the electric fields around charged cylindrical objects.
– **Magnetostatics**: Studying the magnetic fields generated by current-carrying cylindrical conductors.
– Antennas: Modeling the radiation patterns of cylindrical antennas, like dipole antennas or slot antennas.

area of differential surfaces in cylindrical coordinates
area of differential surfaces in cylindrical coordinates

Electromagnetic Field Theory-Lecture 2

video lecture of cylindrical coordinate systems


Also read here


What is the cartesian coordinate system?

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