PHYS 308 Homework
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   Homework #12: Do not turn these in since there is a test next week. I will post my solutions so that you can check your work.

  1. (a) Starting from the integral form of Ampere's Law, derive the general expression for the magnitude of the magnetic field at any location between the radii 'a' and 'b' in the torus Figure 6.49. (b) Starting from the integral form of Faraday's Law, derive the expression for the self-inductance of that same torus. (c) Derive the expression for the self-inductance in that torus assuming that a=1.5cm, b=4.5cm, h=3.0cm, and the current 'I' varies as I=I0sin(ωt) where ω=2πf, f=60Hz, and I0=4.50A. The torus has a total of 75 turns.
  2. problem 7.35
  3. (a) Starting from the integral form of Ampere's Law, derive the expression for the magnetic field inside a cylindrical solenoid of length L and radius 'R' where L>>R. (b) Starting from the integral form of Faraday's Law, derive the expression for the self-inductance of that same solenoid. (c) Calculate the self-inductance of that same solenoid where L=20cm and R=1.5cm. It has a single layer of wire wrapped around it with a total of 1,900 turns. Note: Be sure that you can derive things such as these for many cases, not just the ones that you did here. This is a general ability that you need to develop.
  4. problem 7.9
   That's all for homework #12.