Week 25 (Feb. 12 - 16)

Reading: Finish electric fields and electric potential. Begin capacitance and dielectrics (Chap. 26)

Key Topics: capacitance, calculation of capacitance, capacitors in series and parallel, energy stored in a capacitor, capacitors with dielectrics,
Lab:

Homework Problems: The following problems are due on Tuesday, Feb. 21 at noon.

  1. Spherical capacitor: How much charge will a 1 cm diameter sphere hold if charged using a 12 volt battery? (Answer: the capacitance of a sphere is 4 times pi times epsilon_o times the sphere's radius. The charge is q = CV =13.4 pico-coulombs)
  2. Adjustable parallel plate capacitor: One side of a parallel plate capacitor is attached to a grounded metal pipe using a copper wire. The other side is attached to the positive terminal of a 1 kV power supply. The circular plates of the capacitor have a radius of 10 cm, and they are 1 mm apart. How much charge (and what sign) is on each plate? (Answer: Using q = CV and C = epsilon_o A / d, we get q = 28 micro-coulombs)
    • If the plate spacing is doubled while the power supply is still connected, then what happens to the charge on each plate? Hint: is the voltage difference across the plates still the same? (Answer: if the plate spacing is doubled, the capacitance is halved, and the charge is halved, since the voltage remains the same.)
    • If the power supply is instead disconnected before the plate separation is doubled, what happens to the charge on the plate? Is the voltage difference across the plates still the same? (Answer: If the spacing is doubled, the capacitance is halved. But if the power supply is removed, then the charge must remain the same (28 micro-coulombs). Therefore the voltage is now doubled to 2000 volts.)
  3. Transferring charge: Suppose you have four identical metal spheres, each with a capacitance of 1 micro-farad. You use a 100 volt power supply to charge up the first sphere. This sphere is briefly touched to the second. The second is then briefly touched to the third. Finally, the third is briefly touched to the fourth. At the end of this process, what is the charge on each sphere and what is the voltage of each sphere? (Answer: the first sphere initially has a charge of 100 micro-coulombs. After touching the second, the first and second each now have a charge of 50 micro-coulombs and a voltage of 50 volts. After touching the second to the third, each of these has a charge of 25 micro-coulombs and a voltage of 25 volts. After touching the third to the fourth, each of these has a charge of 12.5 micro-coulombs and a voltage of 12.5 volts )
General College Physics