1. Electric fields in Material Space
Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I
Electric fields in Material Space
Sandra Cruz-Pol, Ph. D.
INEL 4151 ch 5
Electromagnetics I
ECE UPRM
Mayagüez, PR
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2. Last Chapter: free space NOW: different materials
Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I
Last Chapter: free space NOW: different materials
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3. Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I
Some applications
superconductors
High permittivity dielectrics
Transistors
Electromagnets
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4. We will study Electric charges:
Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I
We will study Electric charges:
Conductors or Insulators
Depends on Frequency and Temperature…
Boundary conditions
Insulators
(dielectrics)
Conductors
(metals)
Semiconductors
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5. Current Units: Amperes [A]
Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I
Current Units: Amperes [A]
Definition: is the electric charge passing through an area per unit time.
Current Density, [A/m2]
The current thru a perpendicular surface:
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6. Depending on how I is produced:
Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I
Depending on how I is produced:
There are different types of currents.
Convection- I flows thru isolator: liquid, gas, vacuum.
Doesn’t involve conductors,
doesn’t satisfies Ohm’s Law
Conduction- flows thru a conductor
Displacement (ch9)
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7. Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I
Current in a filament u
Convection current, [A]
Convection density, A/m2 Dl DS rv
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8. Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I
Conduction Current
Requires free electrons, it’s inside conductor.
Suffers collisions, drifts from atom to atom
Conduction current density is:
Newton’s Law
where rv=ne
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9. Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I
20oC
Low frequency
Conductivity (S/m)
Silver
6.1 x 107
Copper
5.8 x 107
Gold
4.1 x 107
Aluminum
3.5 x 107
Carbon
3 x 104
Sea water 4
Silicon
4.4 x 10-4
Pure water
10-4
Dry Earth
10-5
Glass, Quartz
10-12, 10-17
Appendix B
Conductors- have many free electrons available.
Colder metals conduct better.
(superconductivity)
semiconductor
Insulators at most lower frequencies.
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10. Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I
A Perfect conductor
Has many charges that are free to move.
Therefore it can’t have an E field inside which would not let the charges move freely.
So, inside a conductor
Charges move to the surface to make E=0
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11. Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I
Resistance
If you force a Voltage across a conductor:
Then E is not 0
The e- encounter resistance to move E I S l V
+ -
rc=1/s= resistivity of the material
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12. Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I
Power in Watts
=Rate of change of energy or force x velocity
Joule’s Law
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13. PE 5.1 Find the current thru the cylindrical surface
Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I
PE 5.1 Find the current thru the cylindrical surface
For the current density
Stroked by lightning
NOTE: 0.1 A is enough to kill a person if not given immediate assistance
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14. Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I
PE 5.2 In a Van de Graaff generator, w=0.1m, u=10m/s and the leakage paths have resistance 1014 W.
If the belt carries charge 0.5 mC/m2, find the potential difference between the dome and the base.
w= width of the belt
u= speed of the belt
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15. PE 5.3 The free charge density in Cu is 1.81 x 1010C/m3..
Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I
PE 5.3 The free charge density in Cu is 1.81 x 1010C/m3..
For a current density of 8 x 106 A/m2, find the electric field intensity and the drift velocity.
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16. Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I
Permittivity
Not really a constant!
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17. Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I
PE 5.6.A parallel plate capacitor with plate separation of 2mm has a 1kV voltage applied to its plane.
If the space between its plates is filled with polystyrene, find E and D.
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18. Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I
Continuity Equation
Charge is conserved.
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19. Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I
Boundary Conditions
We have two materials
How the fields interface?
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20. Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I
Boundary Conditions
We have two materials
How do the fields interface?
We look at the tangential and the perpendicular component of the fields.
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21. Cases for Boundary Conditions:
Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I
Cases for Boundary Conditions:
Dielectric- dielectric
Conductor- Dielectric
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22. Dielectric-dielectric B.C.
Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I
Dielectric-dielectric B.C.
Consider the figure below:
E1n E1 q1 a b c d
D w Dh e1
E1t
E2n e2 E2
E2t
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23. Dielectric-dielectric B.C.
Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I
Dielectric-dielectric B.C.
Consider the figure below:
D1n D1 Dh
D S rS
D1t e1
D2n D2 e2
D2t
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24. Conductor-dielectric B.C.
Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I
Conductor-dielectric B.C.
Consider the figure below: En E q1 c d e1 Et
dielectric
conductor Dh
s2=∞
E2=0 a b
D w
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25. Conductor-dielectric B.C.
Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I
Conductor-dielectric B.C.
Consider the figure below: En E q1
D S e1 Et
dielectric
conductor Dh rS
s2=∞
E2=0
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26. Summary B.C. Dielectric-dielectric Dielectric-conductor
Because E=0 inside the conductor.
Tangential Normal
Tangential normal

27. Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I
PE A homogeneous dielectric (er=2.5) fills region 1 (x<0), while region 2(x>0) is free space.
Find
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