1. Electricity and Magnetism INEL 4151
Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I
Electricity and Magnetism INEL 4151
Sandra Cruz-Pol, Ph. D.
ECE UPRM
Mayagüez, PR
Electrical Engineering, UPRM (please print on BOTH sides of paper)

2. Topics Electric Fields, [Coulomb’s Law], Gauss’ Law, E, D, V)
Convection/conduction current, conductors, Polarization in dielectrics, Permittivity, conductors,[§ ] resistance, capacitance [§6.5]
Magnetic fields [Biot Savart Law], Ampere’s Law,
Flux Density, Magnetic Potentials , [§ , 7.7]
Magnetic Force, torque, moment, dipole, inductors,
Magnetic circuits [§ , , 8.8, 8.10] Faradays Law, Transformer & Motional emf,
Electromagnetic Waves: Maxwell Eqs., time varying potentials and Time Harmonic fields [§ ]
waves in different media, power and Poynting vector,
Incidence at normal angles. [§ ]
Transmission lines: Parameters, equations, Input impedance, SWR, power,
Smith Chart [§ ]

3. Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I
Electrical Engineering, UPRM (please print on BOTH sides of paper)

4. Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I
Some terms
E = electric field intensity [V/m]
D = electric field density or flux
H = magnetic field intensity, [A/m]
B = magnetic field density, [Teslas]
Electrical Engineering, UPRM (please print on BOTH sides of paper)

5. Vector Analysis Review:
Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I
Vector Analysis Review:
What is a vector?
How to add them, multiply, etc,?
Coordinate systems
Cartesian, cylindrical, spherical
Vector Calculus review
Electrical Engineering, UPRM (please print on BOTH sides of paper)

6. Vector A vector has magnitude and direction.
In Cartesian coordinates (x,y,z):

7. Vector operations
Commutative
Associative
Distributive

8. Example Given vectors A=ax+3az and B=5ax+2ay-6az (a) |A+B| (b) 5A-B
Answers: (a) 7 (b) (0,-2,21)

9. Vector Multiplications
Dot product
Cross product
Note that:

10. Also… Multiplying 3 vectors: Projection of vector A along B: Scalar:

11. Example Given vectors A=ax+3az and B=5ax+2ay-6az
(c) the component of A along y
(d) a unit vector parallel to 3A+B
Answers: (c) 0 (d) ± (0.9117,.2279,0.3419)

12. Coordinates Systems Cartesian (x,y,z) Cylindrical (r,f,z)
Spherical (r,q,f)

13. Cylindrical coordinates (r,f,z)

14. Spherical coordinates, (r,q,f)

15. Vector calculus review
Del (gradient)
Divergence
Curl
Laplacian
(del2 )
Cartesian
Coordinates

16. Theorems
Divergence
Stokes’
Laplacian
Scalar:
Vector:

17. Vector calculus review
Del (gradient)
In Other
Coordinate
systems