Question

Consider two infinite plates, both parallel to the xy plane of a coordinate system. The top plate is at the height z = +5cm and carries a uniform charge distribution of ?= +3nC/m2. The bottom plate is at height z = - 5cm and carries a uniform charge distribution of ?= -3nC/m2. The space between the plates is filled with air. Between the plates runs a long wire along the y-axis (at z=0 and x=0), carrying a current of 10A. Two 1C test charges are moving between the plates. Test charge 1 moves in y-direction at a height of z = +2cm, at a speed of 4x106 m/s. Test charge 2 moves in x-direction at a height of z = -2cm, at a speed of 3m/s. (a) Calculate the electric field between the plates and the magnitude and direction of the electric force FE exerted on each of the test charges due to that electric field. (b) Calculate the magnitude and direction of the magnetic field caused by the current through the wire at the location of the test charges, and the magnitude and direction of the magnetic force FM exerted on each of the test charges due to that magnetic field. (c) Combine the electric and magnetic forces to find the magnitude and direction of the total force on each of the test charges.

Answer #1

a. Consider two infinite sheets parallel to the xy
plane, separated by distance d, carrying charge densities
+? and -?. Solve for and sketch the potential as
a function of z.
b. Consider two disks of radius R parallel to the
xy plane, centered on the z axis and separated by
distance d, carrying charge densities +? and
-?. (In a real capacitor, the charge density will not be
strictly uniform, but we will continue to ignore that for the...

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