Homework 8
Grant & Phillips 3.8, 4.3, 4.4, 4.9
5) An electron travelling with a velocity of 107i m/s enters the region between a pair of capacitor plates. The plates are squares, 10cm on a side, separated by 1cm in the z direction and have a potential of 1V between them (below). Describe the path of the electron as passes between the plates and find the angle at which it leaves the plates. You may assume that the field between the plates is uniform.
6) A wire carrying a current I lies along the z axis with the current flowing in the positive z direction. Verify the Ampere's Law holds for the rectangular path (-2, -1, 0) to (2, -1, 0) to (2, 1, 0) to (-2, 1, 0) and back to (-2, -1, 0). (Hint, with a little care you need do only 1 line integral.)
7) A very long straight wire of radius R carries a high-frequency alternating current. For reasons that we may come to understand, this means that the current is confined to a thin layer near the surface of the wire (skin effect). Assuming that the high-frequency has no other effect on the magnetic field, compute the magnetic field inside and outside the wire if the current density at radius r (< R) is given by J = J0 exp((r-R)/d) where d, the skin depth, is smaller than R.
8) Here is our old friend the six funny fields. This time explain which ones have zero curl and which non-zero and how you know.
