Two infinite sheets of current flow parallel to the y-z plane. The left-hand sheet, which intersects the x-axis at x = 0, consists of an infinite array of wires parallel to the z-axis with a density n = 910 wires/m and a current per wire of IL = 0.17 A in the +z direction. The right-hand sheet, which intersects the x-axis at x = a = 12 cm, is identical to the left-hand sheet, except that it has a current per wire of IR = 0.17 A in the -z direction.
a) Calculate the y-components of the net magnetic field in the following places: x1 = -15 cm, x2 = 6 cm, and x3 = 24 cm. (The x- and z-components of the B-field are zero.)
B(x1)y = T
B(x2)y = T
B(x3)y = T
b) Suppose the above configuration of currents is unchanged except that the direction of the current IR is reversed so that now IR also flows in the +z direction. (The magnitude remains the same.) Calculate the y-components of the net magnetic field at the same positions as in part a).
B(x1)y = T
B(x2)y = T
B(x3)y = T
c) Return to the configuration of part a). Suppose you want to have the region 0 < x < a able to confine electrons (qe- = -1.60 x 10-19 C, me- = 9.11 x 10-31 kg) that have been accelerated from rest through a 66 V electrostatic potential. If the electrons are to be stacked in circular orbits parallel to the x-z plane with centers on the plane x = a/2, what is the minimum current per wire required if IL and IR are equal in magnitude but opposite in direction?
IL = A