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Important Vector notations in electromagnetism

div grad S = S2

)S(V)V(S)VS(

curl grad = 0 0)(

1.

2.

3.

4.

E)E()E( 2

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Theorems in vector fields

Gauss Divergence Theorem

It relates the volume integral of the divergence of a vector V to the surface integral of the vector itself.

According to this theorem, if a closed S bounds a volume , then

div V) d = V ds

Sd dsVV )(

(or)

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Stokes Theorem

It relates the surface integral of the curl of a

vector to the line integral of the vector itself.

According to this theorem, for a closed path C bounds a surface S,

s (curl V) ds = V dlC

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Maxwells Equations

Maxwells equations combine the fundamental laws of electricity and magnetism .

The are profound importance in the analysis of most electromagnetic wave problems.

These equations are the mathematical abstractions of certain experimentally observed facts and find their application to all sorts of problem in electromagnetism.

Maxwells equations are derived from Amperes law, Faradays law and Gauss law.

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Maxwells Equations SummaryMaxwells

Equations

Differential form Integral form

1. Equation from

electrostatics

2. Equation from

magnetostatics

3. Equation from

Faradays law

4. Equation from

Ampere

circuital law

D. vs

dvds.D

0. B 0s

ds.B

t

BE

s

ds.t

Bdl.E

t

DEH

sl

ds).t

DE(dl.H

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Maxwells equation: Derivation

Maxwells First Equation

If the charge is distributed over a volume V. Let be the volume density of the charge, then the charge q is given by,

q = v

dv