Review of co ordinate systemsReview of co ordinate systems

All co ordinate system

1. Lec # 2
Review of Co-ordinate Systems
Cartesian, Cylindrical & Spherical Coordinate Systems
Subject: Electromagnetic Fields
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3. Objectives
•To Understand the basics of different coordinate systems
•To Know how to represent a point in different coordinate
systems.
•To Know how to transform variables of one coordinate system
into the other.
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4. Co-ordinate System
A system that is used to represent a point in space.
Types:
1.Rectangular/Cartesian Co-ordinate System
2.Circular Cylindrical Co-ordinate System
3.Spherical Co-ordinate System
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5. Rectangular/Cartesian Co-ordinate System
•In this system, a point ‘P’ is represented by P(x, y, z), where the
three planes x, y and z are perpendicular to each other.
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Fig.1: Cartesian Co-ordinate System

6. Rectangular/Cartesian Co-ordinate System
•Unit Vectors: a
x, a
y
, and a
z
are the unit vectors in the
Cartesian coordinate system, directed along the x, y, and z
axes, respectively, as shown in Fig. 2.
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Fig.2: Unit Vectors in Cartesian Co-ordinate System

7. Rectangular/Cartesian Co-ordinate System
•Practical Example:
–Fitting of screw; the rotation of screw is along x-y axes while
screw itself is along z-axis or screw is being fitted into
direction of z-axis.
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Fig.3: Cartesian Co-ordinate
System Example

8. Circular Cylindrical Co-ordinate System
•It’s 3-D version of polar co-ordinate system (r, ϴ).
•In this system, a point ‘P’ is represented by P( ρ, φ , z ), which
is intersection of three mutually perpendicular surfaces i.e. a
circular cylinder (having radius ‘ρ’ ), a plane (φ) and another
plane (Z).
–ρ -> meters
–φ -> deg or rad
–z -> meters
•Unit Vectors:
– a
ρ, a
φ
, and a
z
.
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Fig.4: Cylindrical
Co-ordinate System

9. Circular Cylindrical Co-ordinate System
•Practical Example:
– An air traffic controller assigns each aircraft certain
cylindrical coordinates, so that controller may know the
location of every aircraft in sky within geographic
boundaries leading to decrease aircrafts crash.
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10. Spherical Co-ordinate System
•It’s a 3-D Co-ordinate System and has no 2D version.
•In this system, a point ‘P’ is represented by P( r, ϴ, φ ), which
is intersection of three mutually perpendicular surfaces i.e. a
sphere (having radius ‘r’ ), a cone (ϴ) and a plane (φ).
–r -> meters
–ϴ -> rad
–φ -> rad
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Fig.5: Spherical Co-ordinate
System

11. Spherical Co-ordinate System
•Unit Vectors:
– a
r , a
ϴ, and a
φ.
•Practical Example:
– Geographical Maps, Latitude and Longitude.
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Fig.6: Unit Vectors in
Spherical Co-ordinate System

12. Relation b/w Co-ordinate Systems
•Relation b/w Rectangular & Cylindrical Co-ordinate Systems
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13. Relation b/w Co-ordinate Systems
•Relation b/w Rectangular & Spherical Co-ordinate Systems
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14. Relation b/w Co-ordinate Systems
•Relation b/w Cylindrical & Spherical Co-ordinate Systems
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tan
-1
r/z

15. Lec # 3
Problems related to Co-ordinate Systems
Subject: Electromagnetic Fields
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16. Co-ordinate Systems
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17. Co-ordinate Systems
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18. Activity
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19. 19

20. Differential Quantities in different Co-ordinate
Systems
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21. Differential Quantities in different Co-ordinate
Systems
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22. Differential Quantities in different Co-ordinate
Systems
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