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Unformatted text preview: introduced at some point, it will experience
force equal to eq. 1
• The ﬁeld does not physically eminate from the object but its
inﬂuence exists at every point in space. The ﬁeld is deﬁned as:
ˆ Gm1
ψ1 = −R 2 (N/kg )
R (2) ˆ
ˆ
where R is a unit vector that points radially away from m1 (−R
points towards m1 ).
• The ﬁeld is shown in Fig. 2.
• How do we ﬁnd the force if the ﬁeld is known?
ˆ Gm1 m2
Fg21 = ψ1 m2 = −R12
2
R12
Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. (3) Electromagnetics I: Introduction: Waves and Phasors 6 ^
R ψ1
m1 Figure 13 Figure 2: Gravitational ﬁeld Ψ1 induced by m1 .
or, if the force on a test mass m is known, then
Ψ= Fg
m Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. (4) Electromagnetics I: Introduction: Waves and Phasors 7 • Electric ﬁelds
This sets the stage for introducing electric ﬁeld . Unlike the gravity
ﬁeld, its source is not mass, but charge, which can be either positive
or negative. Both ﬁelds vary inversely with the square of distance.
• Charge has a minimum value: one electronic charge (e) and is
measured in coulombs (C).
• Electron charge magnitude is
e = 1.602 × 10−19 (C) (5) • Actually, the charge of an electron is considered negative (as
opposed to, e.g., protons) so that electron charge is qe = −e
and the proton in qp = e.
• Two charges of the same polarity repel each other, while those
of opposite polarity attract each other,
Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. Electromagnetics I: Introduction: Waves and Phasors 8 • The force acts along the lines joining the charges,
• The force is proportional to the charges and inversely proportional to the square of the distance between them.
These properties summarized into Coulomb’s law:
ˆ
Fe21 = R12 q1 q2
(N) in free space
2
4π 0 R12 (6) Symbols are similar to the gravity case, except now we have 0 =
8.854 × 10−12 (F/m) which is electrical permittivity of free space and
is measured in Farads/meter (F/m). Fig. 3 illustrates the two point
charge case.
Electrical force also acts over distance and we again deﬁne
electric ﬁeld intensity E due to charge q :
ˆ
E=R q
4π 0 R2 (V/m) in free space as illustrated in ﬁg. 4 for a positive charge
Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. (7) Electromagnetics I: Introduction: Waves and Phasors 9 Fe21
+q2
^
R12 +q1 R12 Fe12 Figure 14 Figure 3: Electric forces between two positive point charges in free
space. ^
R E
+q Figure 15 Figure 4: Electric ﬁeld E due to charge q. Notes based on Fundamentals of Applied Electromagnetics (Ulaby et al) for ECE331, PSU. Figure 15 Electromagnetics I: Introduction: Waves and Phasors 10 Two important observations regarding charges:
1. Conservation of charge: (net) electric charge can neither
be created nor destroyed. Given np positive and nn...
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 Fall '12
 MartinSiderious
 Electromagnet

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