8/25/2015
WHY TAKING THIS COURSE?
MWF 9:30 – 10:20
MSB306

Lee Chow
Department of Physics
University of Central Florida
Orlando, FL 32816

E&M is a well-established field. A complete
theory is available. Through E&M, we can
learn the approach to a problem from
physicist’s point of view.
Electricity & Magnetism I

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ELECTRICITY AND MAGNETISM I
It is important. It can be applied to other
fields. The concept of potential can be used in
gravitational field. The field concept leads to
QED, and the unification leads to the Grand
Unification Theory and superstring theory.
It is useful. Almost all the « Everyday » life
experience of forces deal with E&M.
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Chap. 2 Electrostatics
What we will learn from E&M I ?
• Curvilinear Coordinates
∭
·
Gauss Law
E field is conservative
• Delta Function
Electricity & Magnetism I
• Integral Calculus
E field due to charge density
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• Differential calculus
Coulomb law (point charge)
Electricity & Magnetism I
• Vector algebra
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Chap. 1 Vector analysis and Integral Calculus
∮
· ℓ
⟹
Scalar potential
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4
Poisson’s equation
Chap. 3 Special Techniques
Chap. 4 Electrostatic field in matter
• Separation of Variables
• Spherical Coordinates
• Multiple Expansion
• Surface charge (bound)
σ
• Volume charge (bound)
• Electric displacement
•
5
• Polarization
Electricity & Magnetism I
Electricity & Magnetism I
• Image method
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Mainly mathematics
Relation between
&
·
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1
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Chap 5 Magnetostatics
Chap 6 Magnetic Field in Matter
• Ampere’s law
·
• No magnetic monopole
• Magnetization
• The field of a magnetized object
• The Auxiliary field H
• Vector potential
•
Electricity & Magnetism I
Electricity & Magnetism I
ℓ
• Biot-Savart law
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• Lorentz force law
• Linear and Nonlinear Media
·
(Gauge selection)
•
(Poisson’s Equation)
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8
Review of 2049
∮
·
, • Electric Potential
• Energy density in E field,
• Ohm’s Law
V=IR
• Current and Resistance
·
• Potential
• Dielectric materials,
Electricity & Magnetism I
Electricity & Magnetism I
• Electric field
• Parallel plate capacitor,
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• Coulomb’s Law
• Gauss Law
,
• Capacitance
• Potential relation
• Circuits (AC & DC)
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Maxwell Equations
·
• Magnetic Flux
·
• Lorentz Force
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• ∮
·
·
• ∮
·
·
• ∮
·
• ∮
·
Electricity & Magnetism I
• Faraday’s Law
Electricity & Magnetism I
• Biot-Savart Law
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∮
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• Ampere’s Law
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Major Laws in E&M
.
·
From divergence theorem,
·
·
Electricity & Magnetism I
Electricity & Magnetism I
·
Concept of the Field
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1. Coulomb law
2. Gauss Law
(Point charge)
·
(Charge distribution)
(differential form)
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Relationship between Coulomb law and Gauss law
Gauss law is easier to solve when symmetry is involved.
·
·
=
·
, measures the spread out of
·
In Cartesian Coordinates,
·
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4. Curl of the
field.
Therefore
·
is always true.
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Since the curl of a gradient is always equal to
zero (
, we can see from last
equation that the electric field, can be
expressed as a gradient of a scalar potential:
This also implied that the is a conservative
field,
Electricity & Magnetism I
16
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The integral does not depend on the path
Electricity & Magnetism I
·
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In electrostatic, the curl of field is equal to
zero. We can start with Coulomb law
·
Electricity & Magnetism I
·
The divergence of
the electric field,
field
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·
Electricity & Magnetism I
·
3. Divergence of
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Gauss law and Coulomb law are closely related.
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7. Continuity equation
5. Lorentz force law.
(Magneto-statics)
·
8. Ampere’s Law
·
Electricity & Magnetism I
Electricity & Magnetism I
6. Biot-Savart Law
is
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There is no work done by the B field because
perpendicular to .
This is the magnetic analogy of Gauss Law.
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9. Divergence of the B field
10. Curl of B
From Ampere’s law, ∮
·
·
·
Electricity & Magnetism I
Because there is no magnetic monopole.
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·
·
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