Discuss the below:
1.) A 1 kg steel ball is levitating a few feet above the surface of the earth. A point charge of + 3.3 mC is located somewhere directly above the ball. You correctly guess that the steel ball must be negatively charged with just enough charge so that the coulomb force between ball and point charge is equal and opposite the force due to gravity. You find that the surface charge density, pi. on the ball is -105 mC/m2 and that the ball's diameter measures 10 cm.
a. What is the distance between point charge and levitating steel ball? h. How many electrons are on the ball?
c. If you give it a slight nudge upwards (be sure not to ground yourself while doing this) what will the ball do?
2.) a) Find a general expression for the electric field on the z-axis, Ex produced by an annular ring (a washer) of uniform surface charge density p, in free space. The ring is in the z = 0 plane, with inner radius p = a and outer radius p = b.
b) If a = 5 cm and b = 10 cm, what is E. at z = 30 cm, given p, = 500 nC/m2? (4)
c) In the limit of h going to infinity, and a going to zero, the disc becomes an infinite plane. We know the expression for an E field in the presence of an infinite plane of charge. Show that your answer for a) gives you the correct expression for the E field of an infinite plane as b gets huge and a gets tiny. (4)
3.) A electric flux density is given by D = y a, + x2 ay (C/m9.
a) Express D In cylindrical coordinates. (4)
b) Find the total flux passing through a Gaussian cylinder aligned with the z-axis with p= 1 tn. and z goes from -2 to 2 m.