In spherical coordinates, each point is represented by an ordered triple of a distance and two angles, similar to the latitude-longitude system used on Earth. A point P is specified by its coordinates P(r,θ,φ), where r is the distance from the origin and θ and φ are the angular coordinates. Orthogonal surfaces in the spherical coordinate system are generated by keeping r, θ, or φ constant, resulting in a sphere, circular cone, or semi-infinite plane, respectively.

1. NAME : PANKAJ NAKUM
ENROLMENT NO. :-
SUBJECT :- FIELD THEORY (2140909)
TOPIC : SPHERICL COORDINATES SYSTEM
SARDAR VALLABHBHAI PATEL
INSTITUTE OF TEHNOLOGY

2. 2
Spherical Coordinates
In the spherical coordinate system, each point is
represented by an ordered triple: the first coordinate
is a distance, and the second and third coordinates
are angles.
This system is similar to the latitude-longitude system
used to identify points on the surface of Earth.

3. 1-3
Spherical Coordinates

4. 1-4
Spherical Coordinates

5. 1-5
Spherical Coordinates

6. Spherical Coordinates
1-6
Point P has coordinates
Specified by P(r,θ,φ)

7. Differential elements in Spherical
coordinate systems
1-7

8. Dot Products of Unit Vectors in the Spherical
and Rectangular Coordinate Systems
1-8

9. Example: Vector Component Transformation
1-9
Transform the field, , into spherical coordinates and components

10. Constant coordinate surfaces-
Spherical system
1-10
 Orthogonal surfaces in spherical
coordinate system can be generated
as
r=constant
θ=constant
Φ=constant
 θ =constant is a circular cone with z axis as its axis and origin at
the vertex,
 Φ =constant is a semi infinite plane as in the cylindrical system.
 r=constant is a sphere with its centre at the origin,

11. 1-11

12. 1-12