Physics 308 Homework
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Homework #11: Due Saturday, April 19, by 12:00noon.

  1. In class I made the claim that the magnetic field at the center of a number "N" loops of wire of radius "R" was B=Nμ0I/2R. (a) Draw this situation with the wire loops lying in the x-y plane. (b) Starting from the Biot-Savart relation, carefully derive the magnetic field strength at the center of these wire loops. Show all of your steps, including any work you do on your drawing.
  2. problem 7.21
  3. problem 7.23
  4. problem 7.29
  5. problem 7.35
  6. Background: The charge stored in a capacitor is given by Q=CV, where C=κε0A/d, with A=the area of the plates and d is the separation distance between the plates. The energy stored in a capacitor is given by E=(1/2)CV2. In medical emergencies (and on TV/movies) you hear the always-perfect-looking doctors say "Charge to 300!" when talking about the defibrillator. That really means 300 Joules.
    Problem: Assume that one of these capacitors (C=100,000μF) is charged to 400J. It is discharged in a time of 0.10sec. Assume that the discharge is approximately uniform throughout that 0.10sec. The plate deparation d=0.50mm=5.0x10-4m and the dielectric constant be κ=5.5. (a) Find the initial value of the electric field E. (b) Find the magnitude of the Maxwell displacement current density during this discharge.
  7. When a pre-storm cloud moves overhead, Earth's usual electric field (110V/m) can increase by a factor of 15. This can happen in a time of 2 minutes. (a) Find the magnitude of the Maxwell displacement current density during this time. (b) Find the total displacement current between Earth and the cloud during this time. The cloud is approximately circular of 5.0km radius.
   That's all for homework #11.