You only have to know Ohms Law

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You only have to know Ohms Law but you have
to know it bloody well! Wilson Poon Scottish
Universities Physics Alliance and School of
Physics Astronomy The University of Edinburgh
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What do you need to know to repair radios?
You only have to know Ohms Law but you have
to know it bloody well!
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Spotting and exploiting the Ohms Laws of
science education
the (few) things that you could do a lot with
if you know them bloody well

• ? Helping children become better scientists
• enjoying the pleasure of understanding
• using a few principles confidently

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Interlude

• Commercial new book with excellent article on
  Growing scientific citizens in a high-tech world
• Encouraging kids to do science
• Many do not know that they can get a career in
  science (as distinct from technology/engineering)

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You only have to know Ohms Law but you have
to know it bloody well!
The little you have to know (very well!) to do a
lot of science.
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Health Warning
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This talk contains equations!
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• Units
• 2. Waves

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1. Units or the nature of measurement
Is the TGV very fast?
This is a meaningless question!

• Is the TGV very fast compared to
• a car?
• an Intercity 125?
• Concord?

? ? ?
Comparisons involve ratios
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All measurements involve comparisons and
therefore taking ratios.
A measurement a number ? a unit
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Units
If you know the units you know quite a lot
and can work out even more!
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p has no units!
Area has dimensions L2 - units of m2
guess
exact
Square 1 length scale
a2
a2
Rectangle 2 length scales
ab
ab
Circle 1 length scale
a2
Ellipse 2 length scales
ab
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Playing with units gets it right to within an
order of magnitude.
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The difference between mistake and rubbish ...
Marks
Rubbish!
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A key goal of science education is to help pupils
acquire and use ladders of comparison
Atom 0.1 nm (1Å) 10-10 m Bacterium 1 mm 10-6
m Hair 0.1 mm 10-4 m Finger 1 cm 10-2 m Boys
girls 1 m 100 m
Electron 10-30 kg Proton/neutron 10-27
kg Bacterium 10-15 kg (1 pg) . . . Hair 10-6
kg (1 mg) . . . Toddlers 10 kg
Vibration period of C 1 ms 10-3 s Heart beat 1
s 100 s . . . A year ? p ? 107 s . (30
Ms) . . Earth age ? 4 Gyr
Different units are appropriate for different
scales of phenomena.
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The density of liquids and solids
It will take a supercomputer months of
computation to work any of these numbers out.
r ? 103 104 kgm-3 for solids and liquids
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Air 1 kg/m3 ? lots of space between atoms in a
gas
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The smallest bacterium
Mycoplasma genitalium L 0.2 mm, V 0.008
mm3 Smallest genome 0.58 Mbp (mega base pairs)

• 1 Mbp 0.001 mm3
• M. Genitalium genome 0.0006 mm3

The lower limit of life as we know it is limited
by the physical size of the hard disc!
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If you know units very well you can do a
lot of science!
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Waves
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Snapshots of a wave propagating down a string
Time
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Waves and obstacles (diffraction)
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Not much of a shadow
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Snapshots of a wave propagating down a string
Time
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Spatial periodicity Wavelength l length of one
cycle (m) Temporal periodicity Period T time
it takes one cycle to repeat (s) Frequency 1/T
no. of cycles per second (/s Hz)
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Time
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Units m / s
l 1m water waves 1 m/s Sound in air 330
m/s Sound in H2O 1500 m/s Light in air 3 ? 108
m/s (7.5 times round the earth /s)
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Waves in confinement Standing waves
Only certain wavelengths are allowed
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L
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Seeing with waves
Quick experiment ...
(A wave is a ruler!)
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The electromagnetic spectrum
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Battle of Britain radar f 20-30 MHz

• 15-10 m ? only just good enough for aircraft
• (Spitfire wingspan 11 m, length 9 m)

John Randalls magnetron (1940)
f 30 GHz 3 ? 109 Hz l 10 cm
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l 10-15 m
l 10 cm
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3G mobile 2.1 GHz 2.1 ? 109 Hz FM 100 MHz
108 Hz AM (long wave) 200 kHz 2 ? 105 Hz
v 3 ? 108 m/s
3G 15 cm FM 3 m AM 1.5 km
Buildings are no big deal for AM not good for
FM bad news for 3G
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Most bats are insectivores Echo location f
10-100 kHz v fl 330 m/s l 3 cm 3 mm
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Violin G D A E f l Viola C G D
A f/1.5 1.5l Cello C G D A f/3 3l
To get the same standing wave patterns Viola
1.5 ? violin Cello 3 ? violin
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Ideal Viola 1.5 ? violin Cello 3 ? violin
Reality Violin 60 cm Viola 65 cm Cello 124 cm
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How to measure the speed of light with
Distance between melted marshmallows l/2, f
2450 MHz, fl speed of light
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The colour of carrots ...
Matter waves
Einstein
Energy, E, of massive particles and massless
photons (speed c)
m0 0
de Broglie
De Broglie borrowed it for massive particles!
(Got him a PhD and a Nobel Prize.)
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Orange colour of carrot due to b-carotene molecule
22 alternating single/double bonds _at_ length
1Å Houses 22 free electrons
? L 22Å linear box
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22Å
Each level 2e ?? (Pauli Exclusion) ? filled to
n 11
? Coloured carrots!
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Absorption spectrum of b-carotene
700
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Should be colourless
Lengthen b-carotene to give green/blue colour.
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A few basic results in waves can be used to make
sense of a very wide variety of phenomena.
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Conclusion
You only have to know Ohms Law but you have
to know it bloody well!
Identifying the Ohms laws and enabling pupils
to use them confidently and creatively is a key
task in science education!
Thats all, folks!
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