2. INTRODUCTION
In year 1984 James Clerk Maxwell brought
together and extended four basic laws in
electromagnetism such as , Gauss’s Law in
electrostatics, Gauss’s Law in magnetism,
Ampere's Law and Faraday’s Law.
A complete set of relations giving the
connection between the charges at rest
(Electrostatics) and charges in motion( current
Electricity), electric fields and magnetic fields
(electromagnetism) were divided theoretically
and summarized in four equations by Maxwell,
called Maxwell’s Equations
James Clerk Maxwell
1831 - 1879
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3. Current Density
• Current density (J) at a point, within a conductor, is the
vector quantity whose magnitude is the current through
unit area of the conductor, around that point, provided
the area is perpendicular to the direction of flow of the
current at that point.
• J = I/A
• dI = J.dS
• The total current density through the surface S
• I = ∫s J.dS
• Thus the current I is defined as the flux of the
current density vector J through the given area
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5. Conduction Current Density
• Conduction Current Density refers to the amount of
current (charges) flowing on the surface of a
conductor (conduction band) in a time t. This surface
is always parallel to the current flow.
• It obeys Ohm’s Law
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6. Convection Current Density
• Convection current , as distinct from conduction
current ,does not involve conductors and
consequently does not satisfy Ohm's law.
• Electrons in a metal are subject to frequent collisions
with atoms. Electrons accelerated by an electric field
lose their energy through collisions which appears as
heat (Joule or Ohmic dissipation).
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7. • The equation of motion for an electron in the
presence of collisions may be written as
m(dv/dt) = -eE – mνcv
Where ν is the collision frequency. In steady
state, we have
• -eE = mνcv
• Multiplying by –en with n the conduction
electron density, we obtain
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8. Random and Drift Velocities
• Random Velocity : In absence of electric field
the electrons moves randomly with zero net
velocity. It is about 106 m/s.
• Drift Velocity: In presence of electric field
electrons moves randomly with net motion in
the direction opposite net electric field. It is
about 10-5 – 10-4 m/s
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9. Introduction of EM Field
• When an event in one place has an effect on
something at a different location, we talk
about the events as being connected by a
“field”.
• A field is a spatial distribution of a quantity; in
general, it can be either scalar or vector in
nature.
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10. Fundamental Vector Field Quantities
In Electromagnetics
Electric field intensity (E)
SI unit = volts per meter (V/m = kg m/A/s3)
Electric flux density (electric displacement) (D)
SI unit = coulombs per square meter (C/m2 = A s /m2)
Magnetic field intensity (H)
SI unit = amps per meter (A/m)
Magnetic flux density (B)
SI units = teslas = webers per square meter (T = Wb/ m2 = kg/A/s3)
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11. Gauss’s Law of Electrostatics
• Gauss' Law is the first of Maxwell's
Equations which dictates how the Electric
Field behaves around electric charges.
• Gauss' Law states that electric charge acts as
sources or sinks for Electric Fields.
• Gauss' Law can be written in terms of
the Electric Flux Density and the Electric
Charge Density as
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12. Implication of Gauss’ Law
• D and E field lines diverge away from positive
charges
• D and E field lines diverge towards negative
charges
• D and E field lines start and stop on Electric
Charges
• Opposite charges attract and negative charges
repel
• The divergence of the D field over any region
(volume) of space is exactly equal to the net
amount of charge in that region.
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13. Gauss Law for Magnetism
• Gauss' Magnetism law states that the
divergence of the Magnetic Flux Density (B) is
zero.
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14. Implication of Gauss Law for
Magnetism
• Magnetic Monopoles Do Not Exist
• The Divergence of the B or H Fields is Always
Zero Through Any Volume
• Away from Magnetic Dipoles, Magnetic Fields
flow in a closed loop. This is true even for
plane waves, which just so happen to have an
infinite radius loop.
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15. Faraday’s Law of Electromagnetic
Induction
• The instantaneous emf induced in circuit is
directly proportional to the time rate of
change magnetic flux through it.
• Faraday's law shows that a changing magnetic
field within a loop gives rise to an induced
current, which is due to a force or voltage
within that circuit.
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16. Implication of Faraday’s Law of
Electromagnetic Induction
• Electric Current gives rise to magnetic fields.
Magnetic Fields around a circuit gives rise to
electric current.
• A Magnetic Field Changing in Time gives rise
to an E-field circulating around it.
• A circulating E-field in time gives rise to a
Magnetic Field Changing in time.
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17. Ampere’s Circuital Law
• the curl of the magnetic field is equal to
the Electric Current Density
• A flowing electric current (J) gives rise to a
Magnetic Field that circles the current
• A time-changing Electric Flux Density (D) gives
rise to a Magnetic Field that circles the D field
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18. Maxwell’s Modification to
Ampere’s Circuital Law
• For time-varying currents, Ampère’s law is not true.
• Maxwell fixed this problem by making a postulate
that is, in a way, the complement of Faraday’s
postulate that a changing electric field produces a
magnetic field; Maxwell proposed that a changing
electric field induces a magnetic field. In particular,
he proposed that
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19. Maxwell’s Equation in Differential
Form
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