maxwell’s equations and inductance intropages.erau.edu/~snivelyj/ps250/ps250-lecture25.pdf · ps...
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PS 250: Lecture 25 Maxwell’s Equations
and Inductance IntroJ. B. Snively
November 2nd, 2015
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Maxwell’s Equations
I⇥B · d⇥l = µ
o
✓iC
+ �o
d�E
dt
◆
encl
I�E · d�l = �d�B
dt
I⇥E · d ⇥A =
Qencl
�o
I�B · d �A = 0
Gauss’s Law:(E Field)
Gauss’s Law:(B Field)
Ampere’s Law:(B Field)
Faraday’s Law:(E Field)
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Today’s Class
Mutual InductanceSelf InductanceSummary
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Imagine: Two Coils
Changing current in Coil 1 produces a changing magnetic field, and an
electromotive force in Coil 2:
E2 = �N2d�B2
dt
Define Mutual Inductance M:
N2�B2 = Mi1
Write flux in terms of i1:
E2 = �N2d�B2
dt= �M
di1dt
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Mutual InductanceIs a constant describing the magnetic flux coupling
between two coils, in terms of current:
M =N2�B2
i1=
N1�B1
i2
Induced electromotive force in one coil is then proportional to the changing current in the other
coil, and the Mutual Inductance “M”:
E2 = �Mdi1dt
E1 = �Mdi2dt
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Mutual Inductance
Constant relating the induced electromotive force (and thus magnetic flux) in one coil with the changing current through another.
Units “Henrys” (for Joseph Henry):
1 Henry = 1 Weber / Amp = 1 Volt * Second / Amp
1 Henry = 1 Ohm * Second = 1 Joule / Ampere2
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Today’s Class
Mutual InductanceSelf InductanceSummary
![Page 8: Maxwell’s Equations and Inductance Intropages.erau.edu/~snivelyj/ps250/PS250-Lecture25.pdf · PS 250: Lecture 25 Maxwell’s Equations and Inductance Intro J. B. Snively November](https://reader033.vdocuments.us/reader033/viewer/2022042020/5e777317f5cda94ac91ccbec/html5/thumbnails/8.jpg)
Imagine: One Coil
Current through the coil produces a changing
magnetic field, leading to electromotive force:
Define Self-Inductance L:
Write flux in terms of i:
E = �Nd�B
dt
N�B = Li
E = �Nd�B
dt= �L
di
dt
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Self Inductance
Induced electromotive force in is then proportional to the changing current in the
coil, and its Self-Inductance “L”:
Is a constant describing the magnetic flux through a coil, in terms of current:
L =N�B
i
E = �Ldi
dt
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Inductors
Used as circuit elements, as they oppose changes in current. Basis for filters (but that would require us to discuss AC properties...)
Exhibit inductance also in units “Henrys”.
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Summary / Next Class:
Mastering Physics for Friday
Work on Homework for Friday