E =
dE =
k l dx
kl
x2 = - x
d
d
.
kl
= 0-
d
Check units: [] = charge/length, so [k / d] has units of
= kl
d
charge
[k]
length 2
=
q
k
2
r
. Units check!
In 2D problems where the E-field has components along x and y, break the problem up into x-

One last important fact about charges and E-fields: The E-field anywhere is always due to all the charges
everywhere. To get the total E-field, must always add up all the E-fields due to all charges everywhere:
Etot = E1 + E2 + E3 + You cannot destroy or

Electric Field Line
The electric field can
field line diagram.
show the E-field at a
individual points (lef
indicate the field
field line diagram
neutral object (coke can or block of wood)
Diagrams
be represented by a
Instead of trying to
whole bunch of
+

Lightning
Back page
15(3) Lightning strike seen through a diffraction
grating identifies temperature, current and
magnetic field strength
Magnetic field; electricity;
diffraction
A bolt from the blue
Tony Hargreaves Feature
15(4) Thunderstorm; lightning
E

Woodwind instruments
Peter Main
Feature
16(2) Comparison of the flute, clarinet and oboe.
Bernoulli effect; modes of vibration.
Carry on juggling
Ken Zetie
Filler
16(2) Newtons 3rd law; forces required to juggle three
masses.
Estimating quantities
Ian Lov

y
(Have used the fact that the distance from the origin to Q 2 is 2
r )E1x = E1 , since E1 is along the x-axis.
Q2= 3e
E2
E 2x E 2 cos E 2 cos 45o 0.707 E 2
Q1= +2e
x
E1
2e
3e
+ 0.707 k 2
2
r
2r
e
e
= [2 + 0.707(3 / 2)] k 2 = 3.06 k 2
r
r
E tot,x = E1x +

Generating your own
equations
Ken Zetie
Lateral thinking
Optical fibres
Newtons law of gravitation
15(1) Mechanism of jumping used by froghopper
insects
Force as mass times acceleration;
kinetic energy
Mathskit
15(1) Wave analysis; Fourier synthesis; beat

GPS
Peter Main
14(3) GPS uses atomic clocks, special and general
relativity to determine latitude, longitude and
altitude.
Electromagnetic waves; gravitational
field
Picture page
Around the world in 90
minutes
Feature
14(3) Views from the International Sp

The electric field is not just an mathematical invention; it is real. We cannot (usually) see it or smell it,
but we can feel it. In some situations, you can see an electric field: visible light is a rapidly oscillating
electric field (more on that later

Extreme diamonds
Carol Tear
Feature
14(1)
Physical properties and formation of diamonds; synthetic
diamonds
The path of a light ray
John Avison
Exam talkback
14(1)
Snells law and total internal reflection
Peter Wade-Wright
Crossword
14(1)
Elements; equili

A coulomb is a huge amount of charge: Number N of es in 1 C = ?
N = 1C
e
N=
1C
1C
=
= 6.3 1018
- 19
e
1.6 10 C
Fact 3: Electric charge is conserved. The net charge of an isolated system cannot change. It is impossible
to create or destroy net charge. Exc

A big C is equivalent to two smaller C side by side:
"Proof" :
For capacitors in series:
Cseries =
1
1
1
+
C1
C2
=
C1
C2
Cseries
Capacitors filled with dielectrics
The capacitance C of a capacitor can be increased by placing an insulator ("dielectric") be

A farad is a huge capacitance. For example, suppose we make a parallel plate capacitor with area A = 1
m2 (big) and separation d = 1 mm = 0.001 m. The capacitance is only
o A
(8.85 10
=
d
10- 3
- 12
C =
)(1)
(tiny!)
;
9 10- 9 F = 9 nF
Multi-farad capacito

Use of formulae and functions in a computer spreadsheet
The last 50 years of powered flight; Airbus; Boeing 747; Concorde; stealth bomber
Behaviour of Earths magnetic field and what causes it.
Magnetic field; electricity; magnetic effects of currents; Far

Measuring acceleration
John Avison
Exam talkback
12(3) Synoptic exam questions on electromagnetism
and dynamics
Presenting data
Ken Zetie
Compukit
12(3) Tables of data in a word processor
The Leviathan of Birr
Castle
Bernard Taylor
Just visiting
12(3) His

Capacitors
A capacitor is simply two pieces of metal near each other, separated by an insulator or air. A capacitor is
used to store charge and energy.
A parallel-plate capacitor consists of two parallel plates separated by a distance d, each plate with a

C-1
Force on a Current Loop
New term: "magnetic dipole moment" or "magnetic moment" = a loop of current
magnetic moment = current area
current I = I A
area A
Direction of = direction of area vector A + right-hand rule:
curl fingers of right hand in direct

Fuzzy logic
Hazel Lucas
Feature
16(4) Binary logic; electronic control system; exam
revision
Logarithms
Ian Lovat
Mathskit
16(4) John Napier; straight line graph; logarithmic
scale; decay constant; base of logarithm; orders
of magnitude; natural logarithm

r , where
Ei
r
r
r
r
E total E1 E 2 E3 K
i
E1
r
E1
Q
k 21
r
, E2 = . , etc
Why? Superposition Principle says that if we place a small test charge q near other charges Q 1, Q2, Q3, ,
then the net force on q is
r
r r
Ftotal F1 F2 K
r
r
r
Ftotal F1 F2
K

Currents make B-fields
We have seen that charges make E-fields:
v
dE =
1 dQ
r
4 0 r 2
Currents make B-fields according to the Biot-Savart Law:
I
dl
I
.
v
v 0 I d l r
dB =
4
r2
where 0 = constant = 4107 (SI units).
dB is the element of B-field due to the e

Gauss's Law for B-fields
B-field lines are fundamentally different from E-field lines in this way: E-field lines begin and end
on charges (or go to ). But B-field lines always form closed loops with no beginning or end. A
hypothetical particle which creat

Looking through
telescopes
At a glance
25(2) Galileo, Whirlpool galaxy, Mount Wilson,
Orion nebula, Cerro Tololo, deep field, James
Webb
Helium-3
Ken Zetie
Feature
25(2) Nuclear fusion; isotope; deuterium; energy
Fusion, fission and
radioactivity
Jan Hath

Saturns rings; Cassini spacecraft; ring nebula; Voyager spacecraft, orbital motion
Centre of mass; radial velocity; orbital motion; transit; spectrum; Kepler mission;
Doppler shift
Rotational motion; precession; moment of inertia; nutation; Chandler wobbl

Energy recovery in Formula One
Ken Zetie and Tom
Weller
Feature
24(1)
Power; acceleration; thermodynamics; kers
Finding answers
Carol Tear
Physics online
24(1)
Units; definitions; WolframAlpha; graphs
Vectors in action
Ian Harding
Mathskit
24(1)
Trigonome

Roche de los Muchachos
Observatory
Carol Tear
Feature
23(2) Cassegrain reflecting telescope; William
Herschel telescope; spectrum; spectrograph;
adaptive optics; Whirlpool galaxy
Graphene
Carol Tear
Physics online
23(2) Andre Geim; manipulating atoms
Bloo

Dating teeth
Identifying and explaining physics ideas
Logarithmic graphs
Diffraction
1777 variables + 100 years
Measuring molecular forces
Wet sand
The number e
Electric charge and current
A bright idea: lumens, light bulbs and illuminance
Do NOT try this

Peter WadeWright
Crossword
21(1) Galen; Gay-Lussac; Avogadro; Raman; rotation; Plancks law
high voltage; emission spectra
Refraction to the rescue
Peter Main
Feature
21(1) Snells law; total internal reflection; optical
fibre; inverse square law; SOFAR; un

Ethical issues
Carol Tear
How science
works
20(2) Rights; duties; Marie Curie; radium; TAT;
Chernobyl; Gulf of Mexico oil spill; Manhattan
project; Joseph Rotblat
Understanding fluids:
Nobel Prize, 1910
Peter Main
Feature
20(2) Van der Waals equation; pha