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PS 250: Lecture 25 Maxwell’s Equations
and Inductance IntroJ. B. Snively
November 2nd, 2015
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)
Today’s Class
Mutual InductanceSelf InductanceSummary
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
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
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
Today’s Class
Mutual InductanceSelf InductanceSummary
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
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
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”.
Summary / Next Class:
Mastering Physics for Friday
Work on Homework for Friday