1. Vector & Coordinate systems
ELECTROMAGNETICS I
EL 3001
Vector & Coordinate systems

3. Vector and Scalar
Scalar quantity : quantity that can be explained by only its magnitude
Ex: length, temperature, height, area, voltage, power
Vector quantity : quantity can only explained by its magnitude and direction.
Ex: velocity, acceleration, force, electric field, magnetic field

4. Vektor Vector quantity : expressed by its magnitude and direction.
Unit Vector

5. VECTOR AND VECTOR COMPONENTS
CARTESIAN

6. VEKTOR POSISI DAN VEKTOR JARAK
Position vector:
Distance Vector
-R1
Distance

7. VECTOR ADDITION
C= A + B=B+A

8. VECTOR SUBSTRACTION B
C=A-B A -B
C= A-B= A +(- B)

9. VECTOR MULTIPLICATION
Multiplication by a scalar constant k
Same direction if k positive and opposite direction if k negative
Longer if the absolute value of k >1, and shorter if the absolute value of k <1 kA A

10. VECTOR PRODUCT
dot product: the product of magnitude of the two vectors and cosine of the angle between the them.
A.B=B.A=AB cos qAB
Projection A on B
Length=A cos qAB

11. DOT PRODUCT

12. CROSS PRODUCT

13. CROSS PRODUCT

14. TRIPPLE PRODUCT

15. Determine
Vector A, its magnitude and unit vector of A
Angle that A makes with Y axis
Angle between A and B
Perpendicular distance from the origin to vector B

17. COORDINATE SYSTEMS Cartesian (x,y,z) Cylindrical (r,q,z)
Spherical (r,f,q)

18. CARTESIAN dSz=dx dy az Z dz dSy=dx dz ay dl dSx=dy dz ax dv=dxdy dz dy

19. CYLINDRICAL

20. CYLINDRICAL ELEMENTS

21. SPHERICAL

22. SPHERICAL ELEMENT
Area elements

23. obey right hand cyclic relation
Base Unit Vector
obey right hand cyclic relation