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