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Unformatted text preview: negative
charges, the total is
q = np e − nn e = (np − nn )e (C) (8) 2. Principle of linear superposition: the total vector electric
ﬁeld at a point in space due to a system of point charges is equal
to the vector sum of the electric ﬁelds at that point due to the
• As noted, eq. 7 is valid for free space; what happens if an
electron is introduced inside electrically neutral material?
• This situation is illustrated in Fig. 5.
• Each atom has an electrically positive nucleus and an electron
“cloud” surrounding it.
Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. +
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+ -+ -+ -+ -+ -+ -+ - - +- - + + ++- +- + -+ -+ +- + - -+ -+ -+ + - + - - -+ + - -+ -+ - -+ -+ + + q + - - + +- - + +- - -+ +- +- +- + - +- +- - -+ +- +- - +- + + +- 11 +- - - +- + + - +- + -+ Electromagnetics I: Introduction: Waves and Phasors + + Figure 1-6 Figure 5: Polarization of atoms in a dielectric material.
• Each atom is electrically neutral.
• After introducing positive charge ⇒ diﬀerent forces cause the
atoms to become distorted.
• Now we can talk about one end (pole) of atom becoming more
positive while the other becomes more negative ⇒ this eﬀect is
called polarization and the atom is now a electric dipole . Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. Electromagnetics I: Introduction: Waves and Phasors 12 Observe that:
• The amount of polarization depends on the distance between
the atom and the point charge,
• The orientation of the dipole is such that the dipole axis is
directed toward the point charge, as illustrated in ﬁg. 5.
• The electric dipoles tend to counteract the electric ﬁeld from the
• The electric ﬁeld inside the material is diﬀerent than in free
space Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. Electromagnetics I: Introduction: Waves and Phasors 13 The form of eq. 7 describing electric ﬁeld is still valid, but we need
to change the electrical permittivity so that
4π R2 = r0 (F/m) (9) is dimensionless quantity called relative permittivity or dielectric constant of the material. What are some typical values?
See Appendix B.
Later on we will use additional quantity electric ﬂux density D =
E (C/m2 ). Electric ﬁeld E and electric ﬂux density D constitute one
of the two fundamental pairs of quantities in electromagnetics. Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. Electromagnetics I: Introduction: Waves and Phasors 14 • Magnetic ﬁelds
• Experimental observation of magnetism goes way back in history
(Greeks 800 B.C.).
• Observation of the magnetic force direction led to realization
that magnetic ﬁeld lines enter magnets at two points: north
and south poles, independent of magnet’s shape.
• Magnetic ﬁeld lines for a bar magnet are given in ﬁg. 6.
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This note was uploaded on 09/25/2013 for the course ECE 331 taught by Professor Martinsiderious during the Fall '12 term at Portland State.
- Fall '12