Sample questions for the second test

1) A 2 nC charge is located on the x-axis at x=3cm. A 3 nC charge is located on the negative y-axis at y=-5 cm. What total force do these two charges exert on a -4nC charge located at x=-2cm, y=3cm, z=1cm?

2) A great big slab of charged matter, with charge density rho, lies on top of the xy plane, between z=0 and z=a. A great big slab of metal, parallel to the xy plane, lies between z=b and z=c, where b>a and c>b. What is the electric field everywhere in space?

3) A 3 microcoulomb positive charge sits at the origin. You are given a -2 microcoulomb point charge and asked to locate it such that the electric field is zero at x=1cm, y=0, z=0. Is the electric field zero anywhere else? If so, where? Now, reposition that negative charge so that V=0 at x=1cm, y=0, z=0. Is the potential zero anywhere else? If so, where?

4) The two AAA batteries in your remote control are dead, and all you have in the house are AA batteries. These don't fit into the battery compartment on your remote control. Can you nevertheless use them to power your remote? If so, how do you hook them up? If all you have in the house is six-volt lantern batteries, could you use them to power your remote? If so, how?

5) A solid conducting sphere or radius a, carryinga total charge of Q, sits at the center of a hollow, neutral conducting spherical shell of inner radius b and outer radius c. What is the electric field everywhere? What is the charge density everywhere? What is the electric potential everywhere?

6) Suppose you have a point charge Q at the center of a ball of negative charge whose charge density is b cos(pi r/R) out to radius r=R, and zero elsewhere. The total charge in this charge distribution is zero; find b in terms of Q, R, and known quantities. Then find the electric field everywhere in space.

7) A six-volt battery is connected to a lamp whose filament has a resistance of 0.4 ohms. How much energy has been drained out of the battery after one hour?

8) Three charged particles are hanging from the same point with the same length of string.   How could you arrange the charges on these masses such that two masses hang at equal angles from vertical and the third hangs straight down.   On what does the value of that angle depend?

9) How could you create a uniform electric field that would suspend in space an oil drop of radius, r, charge q and mass density r ?

10) Consider a point charge of 15nC, and take V=0 at infinity. What are the shape and dimensions of an equipotential surface having a potential of 30 V due to q alone?   Are the surfaces whose potentials differ by a constant amount evenly spaced?   What if you had two charges of 15nC separated by 5cm?