Laser Imaging Laboratory : www.chosun.ac.kr/~yjshin

Professor of Physics, Chosun University

yjshin@chosun.ac.kr 82-62-230-6638

Yong-Jin Shin, Ph.D.

ELECTROMAGNETICS - II

— ELECTROMAGNETICS —

1. Vector Analysis

2. Electrostatic Field in Vacuum

3. the Electrostatic Field; Energy and Potential

4. Conductors in Vacuum

5. Dielectric Materials

2nd semester

1st semester

6. Electric Current

7. Magnetic Fields

8. Magnetic Circuits

9. Electromagnetic Induction and Inductance

10. Electromagnetic Field

ROUGH COURSE CONTENTS (2nd semester)

EXAM : will be given during midterm- and final-exam week

6. Electric Current

7. Magnetic Fields

8. Magnetic Circuits

9. Electromagnetic Induction and Inductance

10. Electromagnetic Field

LITERATURES :

Schaum’s Outline of Electromagnetics –Joseph A. Edminister– McGraw-Hill (2011)

Introduction to Electrodynamics-David J. Griffiths-Pearson(2014)

Classical Electrodynamics– J.D. Jackson – John Wiley & Sons

전기자기학 – 심광열 외 공저 – ㈜북스힐 (2008)

전자기학의 기초 – 신용진외 공저– ㈜북스힐

Outline and Object of Subject

Electromagnetic theory, together with classical and quantum

mechanics, forms the core of present-day theoretical training

for undergraduate and graduate physicists. A thorough

grounding in these subjects is a requirement for more

advanced or specialized training.

Typically the undergraduate program in electricity and

magnetism involves two semesters beyond elementary physics.

with the emphasis on the fundamental laws, laboratory

verification and elaboration of their consequences, circuit

analysis, simple wave phenomena, and radiation. The

mathematical tools utilized include vector calculus, ordinary

differential equations with constant coefficients.

01 week Chapter 6. Electric Current

(1/2) Current Flow, Electric Resistance

02 week Chapter 6. Electric Current

(2/2) Voltage, Power, Thermoelectric Phenomenon

03 week Chapter 7. Magnetic Field

(1/3) Magnetism, Magnetostatic Field

04 week Chapter 7. Magnetic Field

(2/3) Magnetic Potential, Magnetic Dipole

Content of Study

05 week Chapter 7. Magnetic Field

(3/3) Current-produced Magnetic Fields, Magnetic Force

06 week Chapter 8. Magnetic Circuit

(1/2) Magnetization Phenomenon, Demagnetizing Force

07 week

08 week Midterm Examination

Chapter 8. Magnetic Circuit

(2/2) Boundary Condition for Magnetic Material,

Magnetic Circuit

Content of Study

09 week Chapter 9. Electromagnetic Induction and Inductance

(1/3) Faraday’s Law of Induction, Self- & Mutual-Induction

10 week

11 week

12 week Chapter 10. Electromagnetic Field

(1/3) Electromagnetic Waves, Displacement Current

Content of Study

Chapter 9. Electromagnetic Induction and Inductance

(2/3) Induced Electromotive Force, Calculating Inductance

Chapter 9. Electromagnetic Induction and Inductance

(3/3) Energy stored in the Coil, Work by EM Force

13 week Chapter 10. Electromagnetic Field

(2/3) Maxwell’s Equations, Traveling EM Waves

14 week Chapter 10. Electromagnetic Field

(3/3) Reflection and Refraction of Electromagnetic Wave

15 week Final Examination

Content of Study

Chapter 6. Electric Current

yjshin@chosun.ac.kr www.chosun.ac.kr/~yjshin

A. Current Flow

B. Electric Resistance

C. Voltage

D. Joules Heat and Electric Power

E. Thermoelectric Phenomenon

Yong-Jin Shin, Professor of Physics, Chosun University

6.A. Current Flow

1. Moving Charge (e+ ; positive electron) :

Moving in the same direction as the current

2. Current I (or i) is not a vector

3. Current density J (or j) is a vector

Direction of a J is the direction of an I

◈ Definition of Current

• Any motion of charge from one region to another in conducting

materials

◈ Direction of a Current

Current

• The SI unit of current is the ampere. i.e., Current is the amount

of charge flowing through a specified area, per unit time.

electron moving

current direction

(1 ampere = 1 coulomb/sec) dt

dQI

(1/2)

Current

The same current can be produced by

(a) positive charges moving in the

direction of the electric field E or (b)

the same number of negative charges

moving at the same speed in the

direction opposite to E

The current I is the time rate of charge

transfer through the cross-sectional area A.

The randum component of each moving

charged particle’s motion averges to zero,

and the current is in the same direction as

E whether the moving charges are positive.

◈ Microscopic Model of Current

(2/2)

◈ Definition of Current Density

• The current I through an area S depends on the concentration n

and charge q of the charge carriers, as well as on the magnitude

of their drift velocity vd. The current density is current per unit

cross-sectional area.

(ampere/m2) dnqvS

IJ

◈ Current density(vector) vs. Current(scalar)

dSJIS

IJ

SnqvSvnqIvnqJ ddd

Current Density

Drift Velocity / Speed

◈ Drift Velocity / Speed

We can express current in terms of the drift velocity of the moving charges.

Let’s consider the situation, a conductor with cross-sectional area S and an

electric field E directed from left to right. To begin with, we’ll assume that

the free charges in the conductor are negative(−); then the drift velocity is in

the direction opposite to the field.

dvltandenSlQ /)(

Senvvl

nSle

t

QIso d

d

)/(

,

S

IJwhere

en

J

enS

Ivthen d ,,

Cewith 1910602.1,

SenvI d

denvJ

For the current density …….

Steady Current and Charge Conservation

◈ Continuous Equation

Conservation current density

Continuous boundary condition

from steady current dt

dqI

and JdsIs

IJ

then t

J

“Continuous Equation”

(time dependent charge distribution)

0 J If = 0

(time independent charge distribution)

so

dV

tdt

dqsdJ

dVJsdJ

with, Gauss theorem

6.B. Electric Resistance

It is defined as the ratio of the voltage applied to the electric current which

flows through it :

Electrical resistance is the opposition to the passage of an electric

current through that conductor. It varies with types of conductor ,

thickness, length, and temperature.

Resistance and Resistivity

◈ Resistance

(1 = 1 Volt/Ampere) i

VR

R

Vi

◈ Resistivity

If conductor has cross section S[m2] and length l[m], the resistance R is

][S

lR ][ m

l

SR

(definition of resistivity)

Electric Conductivity

Conductivity(k=) varies depending on the material, physical state and

temperature dependent.

◈ Conductivity

◈ Ohm’s Law

The electric current passing through a conductor is directly proportional to the

potential difference across it, and is inversely proportional to the resistance.

S

IJ with

S

lRand

R

VI

l

Vk

l

V

l

S

S

V

RS

VJ

1with

l

VE

]/[ 2mAE

kEJ

so,

11 m

RS

lk

with

R

VI IRV

EkEJ or, 1kwith

1/2

• Conduction electrons in the metal treated with gas molecules.

• Receiving acceleration of mass m electron by electric field (Newton’s 2nd Law)

• Drift velocity / speed

when is the average amount of time it takes to collision then collision,

mEe

mFaamEeEqF

m

eEavd

ne

Jvd

also,

so, Jne

mE

ne

J

m

eE

2

k

JJE also,

then,

dmv

ne

m

nek

221 (with, ; mean free path) dv

◈ Conductivity of Metal

Electric Conductivity 2/2

Temperature Coefficient of Resistance

◈ Temperature Coefficient

Let R0 is the resistance of conductor at temperature 0℃. When 1℃ rise

in the temperature of the conductor, the growth rate of the resistance α0

is the temperature coefficient at temperature 0℃.

][1 00000 tRtRRRt with 5.234

10

Rt is the resistance of the conductor at temperature t℃

][1 tTRR ttT with

t

tT

tR

tT

RR

Rt is the resistance of the conductor at temperature t℃ and RT is the

resistance of the conductor at temperature T℃.

When 1℃ rise from t℃ in the temperature of the conductor, the growth

rate of the resistance αt is the temperature coefficient at temperature t℃.

Electric Resistance and Capacitance

◈ Parallel Plate Capacitor

QndsE

s ‘Gauss’s Law’

◈ Micro Current in the Dielectric

kEEJ

1 Where, ρ : resistivity

k : conductivity

for the dielectric

CVQEdsJdsJSI

ss

111

ks

l

s

lR

RC

CR

I

CV

l

s

RC

◈ Resistors in Series

eqiRRRRiiRiRiR )( 321321

The current i must be the same in all of them.

j jeq RRRRR 321

Equivalent Resistance

◈ Resistors in Parallel

eqRRRRRRRiiii

321321

321

111

The potential difference between the terminals of each resistor must be the same and equal to ɛ

j

jeq RRRRR

11111

321

Equivalent Resistance

Kirchhoff’s Rules

The algebraic sum of the currents into any junction is zero.

◈ 1st Rule (Junction Rule, valid at any junction)

Multi-loop circuit Charge Conservation

0321 j jiiii

at b junction

0321 iii

at d junction

0321 iii

Let out (+) and in (-)

231 iii

(1/2)

The algebraic sum of the potential differences in any loop, including

those associated with emf’s and those of resistive elements, must

equal zero.

Single-loop circuit Energy Conservation

221121 RiRi j jjj j Ri

iR

Let clock-wise (+) and

counter clock-wise (-)

0 iR

Kirchhoff’s Rules (2/2)

◈ 2nd Rule (Loop Rule, valid for any closed loop)