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ELECTROMAGNETISM N. Alan Murray. 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. Syllabus. ® Maxwell's Equations. DON'T PANIC!.

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Presentation Transcript
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

Syllabus

®Maxwell's Equations

Alan Murray – University of Edinburgh

electromagnetic myths and 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

Electromagnetic Mythsand Realities

Alan Murray – University of Edinburgh

electromagnetism some reassurance
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

Alan Murray – University of Edinburgh

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”

A

Formula

Sheet?!?!

Resources

Alan Murray – University of Edinburgh

assumed knowledge
Assumed Knowledge
  • Charge, Voltage, Current
  • Q = CV
  • V = RI and its at-a-point vector equivalent,J = σEsee revision later
  • E = ρJ
  • ρ = 1/σ
  • E = V/d (but we will show that is only occasionally true!)Not much more!

Alan Murray – University of Edinburgh

coulomb s law

Coulomb’s Law

Alan Murray

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

Alan Murray – University of Edinburgh

charges and forces

â

Qa

Qb

r

Fa

Fb

Fa =-QaâQb

4per2

Fb =+QbâQa

4per2

Charges and Forces

NB .. In air, e= 8.85 x 10-12 Fm-1

|â| = 1, Fa = -Fb

Alan Murray – University of Edinburgh

unit vector r

â3

1 unit

â4

â1

â2

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 velocityv =Sâ , 100m/s, North-East (ì)

â = (1/Ö2, 1/Ö2, 0) in this case.

Example on board!

Alan Murray – University of Edinburgh

charges and fields

Where Eb =-Qbâ

4per2

Fa =-QaâQb

4per2

Fb =+QbâQa

4per2

Where Ea= +Qaâ

4per2

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)

Alan Murray – University of Edinburgh

two positive and equal charges

Qa

Qb

Two Positive and equal charges

|E|

|Ea|

|Eb|

Alan Murray – University of Edinburgh

charges and fields14

d

------

+ +++++

+q

F

E

0

V

Voltage V

Charges and Fields

E = -V/d

F = +q(-V/d)

F = qE again

Where E is the field set up inside the capacitor

Alan Murray – University of Edinburgh

charges and fields15

V

0

|E|

0

Charges and Fields

V

E = -V/d

Alan Murray – University of Edinburgh

several charges

+Qc

+Qd

-Qe

+Qa

-Qb

Several Charges?

Ea

Eb

Ec

Ed

Ee

Alan Murray – University of Edinburgh

several charges17

+Qc

+Qd

-Qe

+Qa

-Qb

Several Charges?

Ea

Eb

Ec

Ed

Ee

ETOT

ETOT

Alan Murray – University of Edinburgh

worked example

1M

+1C

+2C

1M

+2C

Worked Example

Ftotal

45°

F on 1C?

Example on board!

Alan Murray – University of Edinburgh

many charges
Many charges …
  • Q1, Q2, Q3 …QN
  • EN = âQN4pe0r2
  • E = E1 + E2 + E3 … EN
  • E = SNEN = SNâQN4pe0r2
  • OK for a handful of charges
  • OK for 1015 electrons/cm3?

Alan Murray – University of Edinburgh

many charges20
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

Alan Murray – University of Edinburgh

charge density 3d

1mm3

Charge Density : 3D

3D

r(r) in C/mm3

1mm3 = r C

r(ra) > r(rb)

Alan Murray – University of Edinburgh

charge density 2d

1mm2

Charge Density : 2D

r(ra) > r(rb)

2D

r(r) in C/mm2

1mm2 = r C

Alan Murray – University of Edinburgh

charge density 1d

1mm

Charge Density : 1D

r(ra) > r(rb)

1D

r(r) in C/mm

1mm = r C

Alan Murray – University of Edinburgh

worked example long straight rod of charge

dE

y

dEy

dEx

R

r

x

dq

Worked ExampleLong straight “rod” of charge

E = (Ex, Ey)

Ex = ∫dEx

Ey = ∫dEy

Alan Murray – University of Edinburgh

worked example long straight rod of charge25

Θ

r

φ

dx

Worked ExampleLong straight “rod” of charge

r

dE

dEy

rdΘ

dEx

R

r

Θ

dq=ρdx

y

x

Alan Murray – University of Edinburgh