PHYS 308 Homework
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   Homework #7: Due Friday, March 20, by 5:00pm.

  1. (a) Derive the expression for the strength of the magnetic field at a given distance 'r' from the axis of a thin straight wirre carrying a current I. Start from the integral form of Ampere's Law and show all of your steps. (b) problem 6.36.
  2. A wire has within it a current density given by J=J0r3z where the boldface z is the z unit vector, and J0=2,500Amp/m5. This will make the current bunch up towards the edges of the wire. The radius of the wire is 0.20cm. Find (a) the magnitude of the magnetic field at a distance of 0.12cm from the axis of the wire, and (b) the magnitude of the magnetic field at a distance of 0.35cm from the axis of the wire.
  3. A hollow wire has within it a current density given by J=J0r3z where the boldface z is the z unit vector, and J0=2,500Amp/m5. The radius of the hollow part of the wire is 0.10cm; the radius of the wire itself is 0.20cm. Find (a) the magnitude of the magnetic field at a distance of 0.12cm from the axis of the wire, and (b) the magnitude of the magnetic field at a distance of 0.35cm from the axis of the wire.
  4. Refer to fig. 6.43 on p. 334 for this problem. Find the strength of the magnetic field at (a) a point 2.5cm above point P, and (b) 6.0cm above point P.
  5. For this problem, recall that I said how you can take what appears to be a complicated problem and simply it with the principle of superposition. Here, the positive x-direction is out of the page, the positive y-direction is to the right of the page, and the positive z-direction is to the top of the page. Three wires are lying on a horizontal surface. All three have the same radius of 1.0mm=1.0x10-3m. They are insulated and are touching. The middle wire is lying at the origin (x,y,z)=(0,0,0). Each has a current of 2.50A running into the page, in the negative x-direction. Find the magntide and direction of the net magnetic field at the following points: (a) (0,0,0) (b) (0,18mm,0) (c) (0,0,35mm) Hint: Perhaps you can make a simplyfying approximation on this one and explain in writing the approximation that made your life easier.
   That's all for homework #7.