文档介绍：Quantum Physics III () Spring 2005
Assignment 1
Feb 2, 2005 Due Feb 9, 2005
Readings
The reading assignment for the first three lectures of is:
• Griffiths, Ch.
• Cohen­Tannoudji, Ch. plement F.
Useful Facts
• 1 atmosphere = × 106 dynes/cm2 (cgs)
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• Msun = × 10 grams
• 1 MeV = × 10−6 ergs (cgs)
Problem Set 1
1. cgs Units for Mechanical and ic Quantities (12 points)
There are several slightly different ways for generalizing cgs units to electro­
ism. The differences revolve around factors of c and 4π. We use units
where Gauss’ Law reads · E = 4πρ and where a factor of c is introduced into
the Lorentz force law so that E and B have the same units. This system is
known as “Gaussian units”. We can just think of it as cgs extended to include
ism.
Find the cgs units — which must take the form — for the following
quantities:
(a) Force
(b) Energy
(c) Surface tension
(d) Pressure
(e) Energy flux (energy per unit area per unit time)
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(f) Electric charge
(g) Electric current
(h) Electric field
(i) ic field
(j) ic flux
(k) Voltage
(l) Conductance
(m) Conductivity
(n) Resistance
(o) Resistivity
(p) Inductance
(q) ic moment
You should be able to deduce the units of ic quantities from the
physical laws that define these quantities in the cgs system:1
e1e2
F12 = 2 rˆ12 Coulomb s Law
r12
e
F = eE + v × B
c
V = dl · E
V = IR Ohms law
R = ρ× length/area
L dI
V = − Faradays law
c dt
4π
× B = j Amperes Law
c
And, recall that the interaction energy of a ic moment µ
in a ic
field is µ · B .
1If you are curious about the factor of 1/c that appears in Faraday’s law, look at Jackson page
820­821 for further discussion.
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2. ic energy density, momentum density and energy flux
(3 points)
If E and B are electric and ic fields, show that:
(a) E 2 and B 2 have the units of energy density,