Cartesian / Rectangular Coordinate System (X, Y, Z) - Field Theory.
A Vector in Cartesian system is represented as (A x , A y , A z ) Or A = A x a x + A y a y + A z a z Where a x , a y and a z are the unit vectors in x, y, z direction respectively. Range of the variables: It defines the minimum and the maximum value that x, y and z can have in Cartesian system. -∞ ≤ x,y,z ≤ ∞ Differential Displacement / Differential Length (dl): It is given as dl = dxa x + dya y + dza z Differential length for a surface is given as: dl = dxa x + dya y --- ( For XY Plane or Z Constant Plane). dl = dya y + dza z , ---( For YZ Plane or X Constant Plane). dl = dxa x + dza z ---( For XZ Plane or Y Constant Plane). Differential length for a line parallel to x, y and z axis are respectively given as: dl = dxa x ---( For a line parallel to x-axis). dl = dya y ---( For a line Parallel to y-axis). dl = dza z , ---( For a line parallel to z-axis). If there is a wire of length L in z-axis, then the differential length is given as...