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course Phy 242
April 30 around 8pm.
110418 Physics IIrotating disk with magnets opposite polarities
spin with drill
use stationary magnet wire coil to generate voltage and thus current
prove since wire mass is equal, current independent of gauge (flux thru area inversely proportional to cs area, length prop cs area)
diameter 4 cm, length 40 meters would imply n = 40 / (2 pi * .04) = 2000 / pi = 700, roughly
4 cm diameter -> area .0004 pi m^2 per loop
total area .28 m^2
alternating field 1 mT, frequency 10 Hz -> flux .00028 T m^2 cnanging in 1/20 sec -> .005 volts, approx..
resistance about 5 ohms => 1 mA, approx..
enhanced with iron core, closer to coil, might get factor of 10 or 100
`q001. That coil contains 25 grams of copper. Copper has a density of about 8 grams / cm^3. How many cm^3 of copper are in that coil?
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Volume = 3cm^3
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`q002. If that coil is 40 meters long, then what is the cross-sectional area of the wire?
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V = length * cs area
Cs area = v/length
(3cm^3) / (40m or 4000cm) = 0.00075cm^2
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`q003. The resistivity of copper is about 1.7 * 10^-8 ohm * meter. Resistance is proportional to length of a uniform wire, because the longer the wire the more spread out the voltage change, hence the less the electric field, and the less acceleration the free electrons in the copper experience. Resistance is inversely proportional to the cross-sectional area of the wire, because the more cross-sectional area, the more electrons are available to be accelerated.
What therefore is the resistance of that coil?
How would your result change if the coil was half as long (but still with the same mass)?
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1.7(10^-8)ohm*m so coil has resistance R = rho*(L/A)
1.7(10^-8)*(40m/0.000000075m^2)
=10 ohm per coil of wire
(the more L, the more R! inverse prop)
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`q004. If the diameter of the coil is 4 cm, what is the area of each loop?
How many loops are there, assuming a 40 meter length?
What therefore is the total area of all the loops?
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A_loop = pi*r^2
=4*pi cm^2
Need to find circumference: pi*(4cm) = n = (40m)/(4*pi cm) = 300 approx
300 loops(4*pi cm^2/loop) = 1200*pi cm^2 = 0.4m^2
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`q005. If the magnetic field inside the coil is .1 Tesla, what is the magnetic flux inside the coil?
If the magnetic field inside the coil changes from 1 milliTesla to -1 milliTesla in 0.1 second, then at what average rate is the magnetic flux changing?
What then is the voltage across the coil?
How much current should result?
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Magnetic field is approx equal to 1 mT at 10 Hz, 20 reversals/sec, 2 reversals for every cycle
Total flux change is (0.001T)*(0.4m^2) = 0.0004Tm^2
Voltage is (0.00047m^2)/(0.05sec) = 0.009 volts [order of 0.01 volts!]
Current: coil resistance is approx 10 ohms, no other significant resistance in circuit so expected current is:
I = (0.01V)/(10ohm)
= 0.001 amps
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`q006. If placing an iron core inside the coil would increase the magnetic field by a factor of 10, how much current would result? Would you be able to detect it?
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`q007. If the magnetic flux could be changed in half the time, how would this affect the current?
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`q008. How much energy should it take to run this circuit during one .1 second transition? What is the average power required during this time?
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`q009. The 25 grams of copper is just a little less than a mole. Each copper atom contributes 2 free electrons. Normally those electrons just sort of bounce around randomly, moving very fast but colliding with atoms and other electrons very frequently. The net result is that that they spend as much time moving in one direction as in any other, and never really get anywhere. A current occurs when there is an electric field in the wire, which tends to accelerate them in one direction along the length of the wire. They don't have much time to speed up before they collide with something and bounce off in a random direction, but the net effect is that the electrons do develop a net drift velocity. (Also, in their collisions, they tend to transfer a little more energy to whatever they bump into, which tends to warm the wire).
How fast, on the average, do those electrons drift through the wire during that 0.1 second flux change?
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&#Good responses. Let me know if you have questions. &#