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Winter wk 3 – Thus.20.Jan.05
Ch.24: Voltage and electric field
Ch.26: Current and resistance
Solar applications
Ch.27: Circuits
Energy Systems, EJZ
Equipotential surfaces and E fields
Equipotential = constant voltage
Conductors are equipotentials, in electrostatics
Potential difference  Electric field
dV/dx = -E or, equivalently, V    E  dr
Practice: Ch.24 Q5,8 (p.646), P#3, 4, 6, 35
Ch.24 #4
Ch.24 #6
Ch.24 #35
Electrostatics (d/dt=0):
charges  fields  forces, energy
 E.dA = q/0=, E = F/q
V (r ) 
 (r ' )
4  
 
d '    E  dl
E   V
W = qV, C = q/V
• Charges make E fields
and forces
• charges make scalar
potential differences
• E can be found from V
• Electric forces move
• Electric fields store
energy (capacitance)
Ch.26: Currents and Resistance
Current = rate of flow of charge
I = dq/dt
Units: amps = coulombs/sec
Current density: J = current/area = n e v
Ch.26 Q1, 2, P.1, 8
Water flow:
Electricity flow:
voltage V
current I
Ch.26: Q1, 2, P.1, 8
Resistance = resistivity * area/length
R =  * A/L
Which conductor has the greatest resistivity?
Ch.26: Q3
Ohm’s law
In many substances, for a given resistance R,
the stronger the driving voltage, the greater
the current that flows:
Voltage = current * resistance
Ch.26 Q5, P.17
Power in electric circuits
Power = rate of energy xfr = voltage*current
units: Watts = volts * amps
Recall that work = qV. Units: J = CV
Solve for V(J,C) =
Then [volts]*[amps] = ____*C/s = ______
If V=IR, find P(I,R) =
Ch.26 #35, 64
P(R,V) =
Ch.27: Circuits:
Battery pumps electricity  current flows
Voltage = emf
Voltage = potential difference
Electromotive force  = V = dW/dq =work
done per unit charge
d/dx = -E = electric field
Emf  and electric field E
d/dx = -E = electric field
Using the fundamental theorem of calculus,
we can derive another of Maxwell’s eqns:
 E
 dx dx   E dx
    E dx
Ch.27: Practice with simple circuits
#5, 14
Solar applications
Storms from the Sun:
p.13: If a CME travels at 1 million miles per hour, how
long does it take to reach Earth?
p.16: The 2 May 1994 event dumped 4600 GW-hr of
electricity into Earth’s upper atmosphere. How much
energy is that in Joules?
p.16: If the Earth’s mean magnetic field is B0=0.5 Gauss,
and one Tesla=104 Gauss, by what percent does 2000
nanoTesla change Earth’s field?
p.54: For the CME of 1 Sept 1859: calculate its speed v,
if it took 18 hours to reach Earth.
more Solar applications
Storms from the Sun:
p.77: If Rsun = 100 REarth, then find the ratio of their
volumes, Vsun/VEarth
p.77: If m=5 millions tons of mass is converted to energy
(E=mc2) each second, calculate the power (P) produced
by the Sun.
p.82: If the Sun’s mass is M=2x1030 kg, and it keeps
losing dm/dt = 5 million tons per second, how long (T)
can the Sun last?
p.83: If the solar wind pours I=1 million amps into Earths
magnetosphere, how much charge (Q) is that per day?
Extra solar applications
p.13: Calculate vthermal from Tsolar wind. Compare to vflow.
p.16: Derive the altitude for a geosynchronous orbit
p.77: If the Sun’s core temperature is about T=107K,
calculate the thermal speed vth of protons in the core.