TUTORIAL 7
MAGNETIC
FIELD IN MATERIAL AND
MAXWELL EQUATIONS
SHI, Liangyu Rm 3121A
lshiac@ust.hk
Department of Electronic and Computer Engineering
HKUST
ELEC 3600
Electromagnetics: From Wireless to Photonic Applications
Outline
1. Magnetic field in Material
•
Self inductance and mutual inductance
•
Magnetic energy
2. Analogy between magnetic field and electric field
3. Maxwell Equations
•
Faraday’s law
•
Displacement current
•
Maxwell’s Equations
ELEC 3600
Electromagnetics: From Wireless to Photonic Applications
Inductance（self）
N turns
solenoid
B∝I, Ψ ∝I, Λ ∝I
Λ =LI
The proportional factor L is called the inductance or self inductance. It
depends on the geometry of the inductor.
Self-inductance [Henry]
or [H]
ELEC 3600
Electromagnetics: From Wireless to Photonic Applications
Mutual Inductance
ELEC 3600
Electromagnetics: From Wireless to Photonic Applications
How to calculate inductance
Given an inductor, we can find the inductance L by:
1. Choose the appropriate coordinate system
2. Assume that the inductor carries a current of I
3. Determine the B-field by applying Biot-Savart’s Law or
Ampere’s Law.
4. Calculate the flux ψ and therefore the flux linkage
5.
ELEC 3600
Electromagnetics: From Wireless to Photonic Applications
Example
ELEC 3600
Electromagnetics: From Wireless to Photonic Applications
Solutions
ELEC 3600
Electromagnetics: From Wireless to Photonic Applications
Magnetic energy
1. This equation suggests that the inductance indicates the energy stored in an
inductor given a current I.
2. This equations explains that why we need to calculate the inductance, that is
the meaning of inductance.
3. This equations suggests a second approach of calculate the inductance.
ELEC 3600
Electromagnetics: From Wireless to Photonic Applications
Faraday’s law
ELEC 3600
Electromagnetics: From Wireless to Photonic Applications
Faraday’s law
The time varying magnetic flux
can be a result of:
1. Stationary loop and time-varying
magnetic field
2. Moving loop in static magnetic
field
3. Moving loop in time-varying
magnetic field
ELEC 3600
A electromotive force(emf) is induced as
the magnetic flux
through the loop
varies as a function of time
Electromagnetics: From Wireless to Photonic Applications
Faraday’s law
ELEC 3600
Electromagnetics: From Wireless to Photonic Applications
Example
ELEC 3600
Electromagnetics: From Wireless to Photonic Applications
Solution
ELEC 3600
Electromagnetics: From Wireless to Photonic Applications
Transformer
ELEC 3600
Electromagnetics: From Wireless to Photonic Applications
Moving loop
ELEC 3600
Electromagnetics: From Wireless to Photonic Applications
Example
ELEC 3600
Electromagnetics: From Wireless to Photonic Applications
Solution
ELEC 3600
Electromagnetics: From Wireless to Photonic Applications
Displacement current
In static electric field. Ampere’s law is for different surface.
ELEC 3600
Electromagnetics: From Wireless to Photonic Applications
Displacement current
ELEC 3600
Electromagnetics: From Wireless to Photonic Applications
Example
ELEC 3600
Electromagnetics: From Wireless to Photonic Applications
Solution
ELEC 3600
Electromagnetics: From Wireless to Photonic Applications
Maxwell equations
ELEC 3600
Electromagnetics: From Wireless to Photonic Applications
Thanks!
ELEC 3600
Electromagnetics: From Wireless to Photonic Applications