introduction to electromagnetism

7/28/2019 Introduction to Electromagnetism

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Electricity Magnetism

Electromagnetism


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Introduction to Electrodynamicsby D. J.Griffith

Engineering Electromagnetic by WilliamH. Hayt & J A Buck

Principles of Electromagneticsby MatthewN. O. Sadiku

Text Books To Be Referred
http://www.oup.co.in/search_detail.php?id=145134


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James Clerk Maxwell Michael Faraday

Electromagnetic Induction

Electromagnetic Waves

Electromagnetism

Light, microwaves, x-rays, and TV and radio

transm issions are al l kinds of electrom agnet ic waves.

They are al l the same kind of wavy disturbance that


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.

A fundamental interactionbetween the magnetic field

and the presence and motionof an electric charge

Electromagnetism

A Field is any physical quantity which takes on

different values at different points in space.
http://en.wikipedia.org/wiki/Fundamental_interactionhttp://en.wikipedia.org/wiki/Electromagnetismhttp://en.wikipedia.org/wiki/Electromagnetismhttp://en.wikipedia.org/wiki/File:VFPt_Solenoid_correct2.svghttp://en.wikipedia.org/wiki/Fundamental_interactionhttp://en.wikipedia.org/wiki/Fundamental_interactionhttp://en.wikipedia.org/wiki/Fundamental_interaction


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Electricity and magnetism are differentaspects ofelectromagnetism

A movingelectric charge

producesmagnetic fields

Changingmagnetic fieldsmove electric

charges


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Charges in motion (an electrical current)

produce a magnetic field

Magnetic field from electricity

A static distribution of charges

produces an electric field


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A changingmagnetic field produces an electric current in a loop surrounding the field

Electricity from changing magnetic

field (Induced Current)

(electromagnetic induction, or Faradays Law)


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The Electricity and Magnetism

A changing magnetic (electric) field produces an

electric (magnetic)field.

Electric (Magnetic)field produces force on charges

An accelerating charge produces electro-magnetic

waves (radiation)

Both electric and magnetic fields can transport energy Electric field energy used in electrical circuits.

Magnetic field carries energy through transformer.


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Waves

A changing electric field can give rise to a changing

magnetic field, and vise versa.

In an electromagnetic wave, the electric and magnetic

fields keep each other going so that it can propagate

through free space.

The energy (E) associated with the em wave is h.Thus

the frequency of oscillation determines the energy that the

wave will carry.

Higher frequency waves such as Gamma rays

carry significantly more energy than smaller

frequency waves like radio waves or visible light.An electromagnetic wave is a transverse wave, with the electric and magnetic fields

oscillating at right angles to each other.


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Electromagnetic

Radiation

Interrelated electric and magnetic fields traveling through space

All electromagnetic radiation travels at speed c = 3108 m/s invacuum. real number is 299792458.0 m/s exactly

Electromagnetic waves travel through empty space!


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An electromagnetic(EM) wave can be

described using

vectors, as it has both

magnitude anddirectional

components

It is a transverse

wave, which means it

vibrates at right

angles to the direction

in which it travels

Properties of Electromagnetic

Waves

This 3D diagram shows a plane

linearly polarized wavepropagating from left to right

with the same wave equations.


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When two or more such waves meet they can

interact in a variety of ways.

If two waves meet, and are of the same

frequency, amplitude and phase, then they willconstructively interfere with each other to

produce a wave with twice the amplitude.

If the two waves met and were out of phase by

180 then they would destructively interfere andtherefore cancel each other out .


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Examples of Electromagnetic Radiation

AM and FM radio waves (including TV signals)

Cell phone communication links

Microwaves

Infrared radiation

Light

X-rays

Gamma rays


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Uses of Electromagnetic Waves

Communication systems

One-way and two-way

Radar

Cooking (with microwaves)

Medical Imaging (X rays)

Night Vision (infrared)Astronomy (radio, wave, IR, visible, UV, gamma)

All that we experience through our eyes is conveyed by

electromagnetic radiation


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The Electromagnetic Spectrum

Relationship between frequency, speed and wavelength = c

Different frequencies of electromagnetic radiation are better suitedto different purposes.

The electromagnetic spectrum is the full range of frequencies orwavelengths at which a wave can oscillate.

The wavelength is the distance a wave will travel during one fullcycle or oscillation. What our eyes detect as visible light areelectromagnetic waves with a wavelength between 750nm and400nm.


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Electrostatics: Charges are at rest(no time-variation)Magnetostatics: Charges are in steady motion(no time-variation)Electrodynamics: Charges are in time-varyingmotion(give rise to waves that propagate and carryenergy and information)

What is Electromagnetic?

ChargeRest Motion


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What is a charge q?


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Three Universal Constants


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Fundamental Relationships
http://localhost/var/www/apps/conversion/tmp/scratch_10/Cartesian%20Coordinate%20System.ppt


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COORDINATE SYSTEMSRECTANGULARCYLINDRICAL SPHERICAL

Choice is based onsym metry of problem

Examples:Sheets - RECTANGULARWires/Cables - CYLINDRICALSpheres - SPHERICAL


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The coordinate surfaces ofthe Cartesian coordinates(x, y, z). The z-axis isvertical and the x-axis ishighlighted in green.Thus, the red plane showsthe points with x=1, theblue plane shows the pointswith z=1, and the yellowplane shows the points withy=-1. The three surfacesintersect at the point P(shown as a black sphere)with the Cartesiancoordinates (1, -1, 1).


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The coordinate surfaces of the

cylindrical coordinates (r, , z).

The red cylinder shows thepoints with r=2, the blue plane

shows the points with z=1, and

the yellow half-plane shows the

points with =60. The z-axis

is vertical and the x-axis is

highlighted in green. The three

surfaces intersect at the point P

with those coordinates (shown

as a black sphere); the

Cartesian coordinates of P are

roughly (1.0, 1.732, 1.0).
http://localhost/var/www/apps/conversion/tmp/scratch_10//upload.wikimedia.org/wikipedia/commons/b/b2/Cylindrical_coordinate_surfaces.png


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Illustration of spherical

coordinates. The red sphere

shows the points with r= 2,

the blue cone shows the

points with inclination (or

elevation) = 45, and the

yellow half-plane shows the

points with azimuth = 60. The zenith

direction is vertical, and the

zero-azimuth axis is

highlighted in green. Thespherical coordinates

(2,45,60) determine the

point of space where those

three surfaces intersect,

shown as a black sphere.
http://localhost/var/www/apps/conversion/tmp/scratch_10//upload.wikimedia.org/wikipedia/commons/a/ad/Spherical_coordinate_surfaces.png


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Cartesian CoordinatesP(x, y, z)

Spherical Coordinates

P(r, , )

Cylindrical Coordinates

P(r, , z)

x

y

z

P(x,y,z)

z

rx

y

z

P(r, , z)

r

z

yx

P(r, , )

Orthogon al Coordinate Systems


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x

z

y

UNIT VECTORS

ji

kUnit Vector

Representation

for Rectangular

Coordinate

System

i

The Unit Vectors imply :

j

k

Points in the direction of increasing x

Points in the direction of increasing y

Points in the direction of increasing z

Rectangular Coordinate System


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Cartesian Coo rd inate

System

x y z

x y z

B B i B j B k

A A i A j A k

cos AB x x y y z zA B A B A B A B A B

Scalar Produc t

AB x y z

x y z

i j k

A B A B sin A A A

B B B

Vector Product

2 2 2

2 2 2

x y z

x y z

A A A A

B B B B

Magnitude of vector

x

y

z

AxAy

AzA

B


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x

y

z

Z plane

x plane

i

j

k

x1

y1

z1

AxAy

Az

),,( 111 zyxA

Base vector p ropert ies

. 1

0

i i j j k k

i j j k k i

i j k

j k i

k i j


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The right-handed Cartesian coordinate system indicating the coordinate planes.
http://upload.wikimedia.org/wikipedia/commons/7/7f/Right_hand_cartesian.svg


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A three dimensional Cartesian coordinate system, with origin O and axis linesX, Yand

Z, oriented as shown by the arrows. The tic marks on the axes are one length unit apart.

The black dot shows the point with coordinatesX= 2, Y= 3, andZ= 4, or (2,3,4).
http://en.wikipedia.org/wiki/File:Coord_system_CA_0.svg


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METRIC COEFFICIENTS1. Rectangular Coordinates:

When a small distance is moved in x-direction, the displacement is dxSimilarly dx and dy can be generated

Unit is in meters


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Cartesian Coordinates

Differential quantities:

Length:

Area:

Volume:

dzzdyydxxld

dxdyzsd

dxdzysd

dydzxsd

z

y

x

dxdydzdv


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AREA INTEGRALS

integration over 2 delta distances

dx

dy

Example:

x

y

2

6

3 7

AREA = 7

3

6

2

dxdy = 16

Note that: z = con stant
http://localhost/var/www/apps/conversion/tmp/scratch_10/Cylindrical%20Coordinate%20System%20F.ppt


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CYLINDRICALCOORDINATES
http://localhost/var/www/apps/conversion/tmp/scratch_10//upload.wikimedia.org/wikipedia/commons/0/0e/Coord_system_CY_1.svg


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The coordinate surfaces of the

cylindrical coordinates (, , z).

The red cylinder shows thepoints with r=2, the blue plane

shows the points with z=1, and

the yellow half-plane shows the

points with =60. The z-axisis vertical and the x-axis is

highlighted in green. The three

surfaces intersect at the point P

with those coordinates (shown

as a black sphere); the

Cartesian coordinates of P are

roughly (1.0, 1.732, 1.0).
http://localhost/var/www/apps/conversion/tmp/scratch_10//upload.wikimedia.org/wikipedia/commons/b/b2/Cylindrical_coordinate_surfaces.png


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Cylindrical Coordinate

Surfaces. The three

orthogonal components, r

(green), (red), and z

(blue), each increasing at a

constant rate. The point is

at the intersection between

the three colored surfaces

VECTOR REPRESENTATION: CYLINDRICAL


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VECTOR REPRESENTATION: CYLINDRICAL

COORDINATES

Cylindrical representation uses: r ,f, z

zzrr aAaAaAA

ff

r r z z A B A B A B A B

UNIT VECTORS:

zraaa f

ScalarProduct

1

1

1

r r

z z

a a

a a

a a

is azimuth angleP (r, , z)


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r

f

z

P

x

z

y

VECTOR REPRESENTATION: UNIT VECTORS

Cylindrical Coordinate System

za

fa

ra


za

Points in the direction of increasing r

Points in the direction of increasing

Points in the direction of increasing z

ra

fa


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METRIC COEFFICIENTSCylindrical Coordinates:

Distance = r df

x

y

dfr

Differential Distances: ( dr, rdf, dz )dris infinitesimal displacement alongr,

r d is along and

dz is along zdirection.

y


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Differential quantit ies:

Length element:

Area element:

Volume element:

r r z z

r z

dl a dl a dl a dl

dl a dr a r d a dz

f

f

f

ff

rdrdasd

drdzasd

dzrdasd

zz

rr

dzddrrdv f

Limits of integration ofr, , are 0


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Show that Volume of a Cylinder of radiusR and height H is

HR

dzdrdr

dzddrrdvV

R H

v

2

0

2

0 0

HR2


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Find out the are of curved surface of a rightcircular cylinder of radius 2m, height 5mand phi is 0 to 2pi.

R is constant,

Radial component of area = dAr

2

2

0 0

20

2

m

R H

dzrddA

H


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Physical systems which have cylindrical

often most conveniently treated by usin

coordinates.

1.Cylindrical capacitor

2.Electric field of line charge.

Appl icat ions

I l t lid l k d t
http://localhost/var/www/apps/conversion/tmp/scratch_10/Spherical%20Coordinate%20System%20F.ppthttp://localhost/var/www/apps/conversion/tmp/scratch_10/Spherical%20Coordinate%20System%20F.ppthttp://localhost/var/www/apps/conversion/tmp/scratch_10//upload.wikimedia.org/wikipedia/commons/d/d9/Coord_system_SZ_0.svghttp://localhost/var/www/apps/conversion/tmp/scratch_10//upload.wikimedia.org/wikipedia/commons/d/d9/Coord_system_SZ_0.svg


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SPHERICAL COORDINATESIn last slides we looked atcylindrical coordinates -- a

system of coordinates

that is very useful whenthe important things about

a three-dimensionalpoint

are its distance from the

z-axis and its angle from

the positive xy-plane.Now we look at situations

in which the important

things about a point are

its distance from theorigin and, using terms

from geography, its

latitude and longitude. In

this situation we use

spherical coordinates.

The f i rs t of these coordinates -- r--
http://localhost/var/www/apps/conversion/tmp/scratch_10//upload.wikimedia.org/wikipedia/commons/d/d9/Coord_system_SZ_0.svghttp://localhost/var/www/apps/conversion/tmp/scratch_10//upload.wikimedia.org/wikipedia/commons/d/d9/Coord_system_SZ_0.svghttp://localhost/var/www/apps/conversion/tmp/scratch_10//upload.wikimedia.org/wikipedia/commons/d/d9/Coord_system_SZ_0.svghttp://localhost/var/www/apps/conversion/tmp/scratch_10//upload.wikimedia.org/wikipedia/commons/d/d9/Coord_system_SZ_0.svghttp://localhost/var/www/apps/conversion/tmp/scratch_10//upload.wikimedia.org/wikipedia/commons/d/d9/Coord_system_SZ_0.svghttp://localhost/var/www/apps/conversion/tmp/scratch_10//upload.wikimedia.org/wikipedia/commons/d/d9/Coord_system_SZ_0.svghttp://localhost/var/www/apps/conversion/tmp/scratch_10//upload.wikimedia.org/wikipedia/commons/d/d9/Coord_system_SZ_0.svghttp://localhost/var/www/apps/conversion/tmp/scratch_10//upload.wikimedia.org/wikipedia/commons/d/d9/Coord_system_SZ_0.svghttp://localhost/var/www/apps/conversion/tmp/scratch_10//upload.wikimedia.org/wikipedia/commons/d/d9/Coord_system_SZ_0.svghttp://localhost/var/www/apps/conversion/tmp/scratch_10//upload.wikimedia.org/wikipedia/commons/d/d9/Coord_system_SZ_0.svghttp://localhost/var/www/apps/conversion/tmp/scratch_10//upload.wikimedia.org/wikipedia/commons/d/d9/Coord_system_SZ_0.svghttp://localhost/var/www/apps/conversion/tmp/scratch_10//upload.wikimedia.org/wikipedia/commons/d/d9/Coord_system_SZ_0.svghttp://localhost/var/www/apps/conversion/tmp/scratch_10//upload.wikimedia.org/wikipedia/commons/d/d9/Coord_system_SZ_0.svghttp://localhost/var/www/apps/conversion/tmp/scratch_10//upload.wikimedia.org/wikipedia/commons/d/d9/Coord_system_SZ_0.svghttp://localhost/var/www/apps/conversion/tmp/scratch_10//upload.wikimedia.org/wikipedia/commons/d/d9/Coord_system_SZ_0.svghttp://localhost/var/www/apps/conversion/tmp/scratch_10//upload.wikimedia.org/wikipedia/commons/d/d9/Coord_system_SZ_0.svghttp://localhost/var/www/apps/conversion/tmp/scratch_10//upload.wikimedia.org/wikipedia/commons/d/d9/Coord_system_SZ_0.svg


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The f i rs t of these coordinates r

denotes the point 's d is tance from the

or ig in. The movie below shows the sets

o f po in ts w ith rho = 0.2, 0.3, ... 1.0.

-- -- .Think of yourself as located at the origin with your right hand


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Think of yourself as located at the origin with your right hand

pointing straight upward along the positive z-axis. Then face

the point in question and lower your right hand until it is

pointing at this point. The angle by which your right hand is

lowered is the coordinate phi. Notice if theta = 0 then the point

is on the positive z-axis; if theta = pi / 2 then the point is in the

xy-plane; and if theta = pi then the point is on the negative z-

axis. The movie below shows points with constant values of

theta for theta = 0, pi / 16, 2 pi / 16, ... pi.

The third coord inate --


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The third coord inate

ph i-- is ident ical to the

coordinate theta used

in cyl indr icalcoordinates. It

measures the angle

from the posi t ive xz-

plane to the po int. Themovie below shows

points wi th constant

values o f theta.

This system o f coo rdinates is very sim ilar to the system --long i tude

and lat i tude-- of coord inates used to descr ibe po ints on the earth's

surface.


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SPHERICAL COORDINATES

r

f

P

x

z

y

Spher ical representation uses: r,, fUNI T VECTORS:

f

aaar

ff aAaAaAA rr

is zenith angle( starts from +Z reaches up toZ) ,

is azimuth angle (starts from +X direction and lies in x-y plane )

P (r, , )

Illustration of spherical
http://localhost/var/www/apps/conversion/tmp/scratch_10//upload.wikimedia.org/wikipedia/commons/a/ad/Spherical_coordinate_surfaces.png


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p

coordinates. The red

sphere shows the

points with r = 2, the

blue cone shows thepoints with inclination

(or elevation) = 45,

and the yellow half-

plane shows thepoints with

azimuth = 60. The

zenith direction is

vertical, and the zero-

azimuth axis is

highlighted in green.

The spherical

coordinates

(2,45,60) determine

r

f

UNIT VECTORS
http://localhost/var/www/apps/conversion/tmp/scratch_10//upload.wikimedia.org/wikipedia/commons/a/ad/Spherical_coordinate_surfaces.pnghttp://localhost/var/www/apps/conversion/tmp/scratch_10//upload.wikimedia.org/wikipedia/commons/a/ad/Spherical_coordinate_surfaces.pnghttp://localhost/var/www/apps/conversion/tmp/scratch_10//upload.wikimedia.org/wikipedia/commons/a/ad/Spherical_coordinate_surfaces.pnghttp://localhost/var/www/apps/conversion/tmp/scratch_10//upload.wikimedia.org/wikipedia/commons/a/ad/Spherical_coordinate_surfaces.pnghttp://localhost/var/www/apps/conversion/tmp/scratch_10//upload.wikimedia.org/wikipedia/commons/a/ad/Spherical_coordinate_surfaces.pnghttp://localhost/var/www/apps/conversion/tmp/scratch_10//upload.wikimedia.org/wikipedia/commons/a/ad/Spherical_coordinate_surfaces.png


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UNIT VECTORS

Spherical Coordinate System

r

f

P

x

z

y

a

fa

ra


Points in the direction of increasing r

Points in the direction of increasing

Points in the direction of increasing ra

fa

a


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Limits of integration ofr, , are 0


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Show that Volume of a sphere of radius R is

2

22

0 0 0

3

3

sin

sin

2 23

4

3

v

R

V dv r dr d d

r dr d d

R x x

R

f

f

34

3R

C CO C S


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Representation of differential length (length element) dl in different coordinate systems:

x y zdl dxa dya dza

r zdl dr a r d a dza

sin rdl dr a r d a r d a

rectangular

cylindrical

spherical

METRIC COEFFICIENTS


dRdl


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Differential quantities:

Length Element:

Area Element:

Volume Element:

dRRddRR

dldldlRld R

sin

dsinRdl

Rddl

dRdlR

ddRdsinRdv

2

RdRd

dldl

sd

dRdsinRdldlsd

ddsinRRdldlRsd

R

R

R

2


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Physical systems which have spherical symmetry are often mostconveniently treated by using spher ical polar coordinates.

1. I f the potential of the physical system to be examined is

spherical ly symmetr ic, then the Schrodinger equation inspherical coordinates can be used to advantage.

2. Electr ic potential of sphere

Applications of Spherical Coordinate
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/laplace.htmlhttp://localhost/var/www/apps/conversion/tmp/L2/Scalar%20and%20Vector%20Fields.ppthttp://hyperphysics.phy-astr.gsu.edu/hbase/electric/laplace.html

introduction to electromagnetism

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