written 7.0 years ago by | modified 2.9 years ago by |
Subject :- Applied Physics 2.
Topic :- Laser.
Difficulty :- Medium.
written 7.0 years ago by | modified 2.9 years ago by |
Subject :- Applied Physics 2.
Topic :- Laser.
Difficulty :- Medium.
written 6.9 years ago by | modified 6.7 years ago by |
In 3 Dimension, the coordinate system can be specified by the intersection of three surfaces. Three commonly used right handed orthogonal coordinate systems are-
2.Cylindrical or circular coordinate system
Cartesian coordinate system: In the cartesian coordinate system all of the three surfaces are planes. The three coordinate axes x,y,and z are mutually perpendicular to each other. In this system, a point P in space is represented by an order triple(x,y,z). These are respectively the distances from the origin to the intersection of a perpendicular dropped from the point P to x,y,z axes as shown in the diagram.the coordinates x,y,and z can be positive or negative.
Cylindrical coordinate systems: In cylindrical coordinates, the surface are two planes and a cylinder. The surfaces used to define the cylindrical coordinates system are
(a) plane of constant z which is parallel to xy plane
(b) A cylinder of radius r with z axis as the axis of the cylinder
(c) A half plane perpendicular to xy plane and at an angle ϕ with respect to xz plane. The angle ϕ is called azimuthal angle.
Figure below shows the cylindrical coordinate system
A point P in space is represented by an order triple (r,ϕ,z). The angle ϕ is measured from the axis and expressed in radians. Anticlockwise measurement of ϕ is treated as positive while clockwise is treated as negative.
Conversion of cartesian to cylindrical coordinates.:
To convert the coordinate of a point from cartesian to cylindrical and viceversa let us consider point P having coordinates P(x,y,z) in cartesian and P(r,ϕ,z) in cylindrical system
Cartesian to cylindrical $(x,y,z) to(r,\Phi,z)$:
$r^2 = x^2 + y^2$
$ tan ϕ =y/x$
z =z
Cylindrical to cartesian $(r,\Phi,z) to (x,y,z):$
$ x = r cos ϕ$
$ y = r sin ϕ$
z =z