ELECTROMAGNETISM N Alan Murray Syllabus Coulomb's Law

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ELECTROMAGNETISMN

• Alan Murray

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Syllabus

• Coulomb's Law
• Gauss's Law
• Potential
• Laplace's Equation
• Capacitance
• Biot-Savart Law
• Ampere's Law

• Curl (L)
• Faraday's Law
• Inductance
• Descriptive only
• Waves in Free Space
• Reflection Standing Waves

Maxwell's Equations
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Maxwell's Equations This is where we are
heading
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Electromagnetic Mythsand Realities

• Electromagnetism is hard
• Electromagnetism is irrelevant to modern
  electronics
• Electromagnetism is very boring

• I'm afraid that it is rather tricky
• Don't be silly, it is fundamental to everything
• I will do my best to render it otherwise!
• analogies
• minimised maths
• worked examples
• song and dance act

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Electromagnetism ...Some reassurance

• Full understanding is possible for
  mathematically- and conceptually- "strong"
  students
• Sufficient understanding
• (in terms of usefulness and exam-passing)
• is possible for all
• There are around 6 possible exam questions!
• this is only slightly flippant

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Resources

• These notes
• Your own additions to these notes
• i.e. listen actively and annotate the notes
• Kraus ("Electromagnetics", McGraw-Hill)
• essential purchase for 3rd and 4th year
• Formula Sheet ...
• provided in exam room
• Worked examples

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Assumed Knowledge

• Charge, Voltage, Current
• Q CV
• V RI and its at-a-point vector equivalent, J
  sEsee revision later
• E ? J
• ? 1/s
• E V/d (but we will show that is only
  occasionally true!)Not much more!

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Coulombs Law

• Alan Murray

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Remember

• Like charges repel one another
• Opposite charges attract one another
• The force of repulsion/attraction get weaker as
  the charges are farther apart.

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Charges and Forces
NB .. In air, e 8.85 x 10-12 Fm-1 â 1, Fa
-Fb
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Unit vector âr?
These are all unit vectors, âi 1 They have a
direction, and a magnitude of 1 â adds direction
to a quantity without changing its
magnitude e.g.... speed 100m/s is a speed
S 100(1/Ö2, 1/Ö2, 0)m/s is a velocity v Sâ ,
100m/s, North-East (ì) â (1/Ö2, 1/Ö2, 0) in
this case.
Example on board!
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Charges and Fields
Fa QaEb
Fb QbEa
Eb(r) is the electric field set up by charge b at
distance r (point a)
Ea(r) is the electric field set up by charge a at
distance r (point b)
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Two Positive and equal charges
E
Ea
Eb
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Charges and Fields
E -V/d F q(-V/d) F qE again Where E is the
field set up inside the capacitor
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Charges and Fields
V
E -V/d
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Several Charges?
Ea Eb Ec Ed Ee
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Several Charges?
Ea Eb Ec Ed Ee ETOT
ETOT
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Worked Example
Ftotal
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F on 1C?
Example on board!
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Many charges

• Q1, Q2, Q3 QN
• EN âQN 4pe0r2
• E E1 E2 E3 EN
• E SNEN SN âQN 4pe0r2
• OK for a handful of charges
• OK for 1015 electrons/cm3?

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Many charges

• For small numbers of charges
• Q1(r1), Q2(r2) QN(rN) is OK to describe a
  charge Q1 at position r1 etc.
• Breaks down as a useful notationfor large N
• Instead use r(r) as the density(in Cm-3) of
  charge at a point r
• SNQN becomes ?r(r)dxdydz ???volr(r)dv

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Charge Density 3D
3D r(r) in C/mm3 1mm3 r C
r(ra) gt r(rb)
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Charge Density 2D
r(ra) gt r(rb)
2D r(r) in C/mm2 1mm2 r C
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Charge Density 1D
r(ra) gt r(rb)
1D r(r) in C/mm 1mm r C
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Worked ExampleLong straight rod of charge
E (Ex, Ey) Ex ?dEx Ey ?dEy
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Worked ExampleLong straight rod of charge
r
dE
dEy
rdT
dEx
R
r
dT
T
dq?dx
y
x