maxwell's equations lecture 1-3

8/2/2019 Maxwell's Equations Lecture 1-3

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Maxwells Equations Preface

Henceforth, we shall examine situations where electricand magnetic fields are dynamic, or time varying. Itshould be mentioned first that in static EM fields,electric and magnetic fields are independent of each

other whereas in dynamic EM fields, the two fields areinterdependent. In other words, a time-varying electricfield necessarily involves a corresponding time-varyingmagnetic field.

Second, time-varying EM fields, represented by E(x, y,

z, t) and H(x, y, z, t), are of more practical value thanstatic EM fields. However, familiarity with static fieldsprovides a good background for understandingdynamic fields.


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Third, recall that electrostatic fields are usually

produced by static electric charges whereasmagnetostatic fields are due to motion of electriccharges with uniform velocity (direct current) orstatic magnetic charges (magnetic poles); time-

varying fields or waves are usually due toaccelerated charges or time-varying currents

Any pulsating current will produce radiation (time

varying fields). It is worth noting that pulsatingcurrent is the cause of radiated emission in digital

logic boards


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As a result of these concepts, Maxwell'sequations will be modified to account for the

time variation of the fields. It should be stressed

that Maxwell's equations summarize the

laws of electromagnetism and shall be the basis

of our discussions in the remaining part of the

course


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Gauss' law tells us lines of Electric flux, are proportional to the electric

field and "diverge" away from a region containing electrical charge.Electric field lines which do not form closed loops begin and end on charge

Gauss' law for magnetism tells us lines of Magnetic field never diverge

from anything, and so must form closed loops. (because there is no

magnetic charge)

Faradays law, tells us electric field lines which form closed loops, encircle(curl) a changing magnetic field.

Amperes law says a couple of things. For the case where the magnetic

field is not changing in time, it says that the magnetic field makes closed

loops around the moving charge that generates the field. If you think of

current flowing through a wire, then the magnetic field would look likecircles centered on the wire and plane described by these circles would be

perpendicular to the wire. If the field varies in time, then another term is

added to the equation which says there is a time varying electric field that

is also giving rise (or fighting) the magnetic field. This term is called the

displacement current and is Maxwell's contribution.
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MAXWELL'S EQUATIONS

Maxwell's equations are a set of fundamental equations that govern all macroscopic

electromagnetic phenomena. The equations can be written in both differential and

integral forms, and here we present both to illustrate applications of some of the

integral theorems discussed in the preceding section.

The General Integral Form


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Notations

is the divergenceoperator

is the curl operator

The Divergence operator

The Curl operator
http://simple.wikipedia.org/w/index.php?title=Divergence&action=edit&redlink=1http://simple.wikipedia.org/w/index.php?title=Operator&action=edit&redlink=1http://simple.wikipedia.org/w/index.php?title=Curl&action=edit&redlink=1http://simple.wikipedia.org/w/index.php?title=Curl&action=edit&redlink=1http://simple.wikipedia.org/w/index.php?title=Operator&action=edit&redlink=1http://simple.wikipedia.org/w/index.php?title=Divergence&action=edit&redlink=1


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EXAMPLES


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Example 1


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Example 2


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Example 2


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Example 3


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Example 3


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Example 4


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Example 4


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Example 5


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Example 5

maxwell's equations lecture 1-3

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