Instructions: Identify all equations and show all intermediate steps in arriving at your answer to each question. If you do not show your work, the instructor reserves the right to deduct points even though you have the correct answer! If I cannot read your work, it's wrong. Use separate sheets of engineering paper for each problem, clearly marking each page with the problem number and your name.

1. Two uncharged metal balls, X and Y, stand on glass rods. A third ball, Z, carrying a positive charge, is brought near the first two. A conducting wire is then run between X and Y. The wire is then removed, and ball Z is finally removed. When this is all done what is the charge on ball X and ball Y.

Discuss the charge exchange process and the charge state of the metal sphere after each step. Use the diagram to the right in your explanation.

2. Consider two charges, q₁ = 50 nC at location (1 cm, 0) and q₂ = - 40 nC at (- 2 cm, 4 cm). Find the position where a third charge Q should be placed for it to feel zero net force.

3. A relatively heavy pith ball in the figure has a mass of 1.5 g and has acquired 1.5 percent of the charge on a thin, ebonite rod by contact. If the charge on the rod is concentrated at one end and the distance of the pith ball from that end is 0.125 meters, what is the charge on the pith ball and the tension in the string? Assume the thread makes an angle of θ = 32^o with respect the vertical?

4. Two uniformly charges rods each with a total charge Q = -7.50 µC and length L = 15.0 cm are arranged as shown below. Find the electric field at P if a = 6.5 cm.

5. Two 1.20-m plastic wires meet at a right angle. One segment carries +3.50 μC of charge distribution uniformly along its length, and the other carries -3.50 μC distributed uniformly along it, as shown in figure below.

a) Find the magnitude and direction of the electric field these wires produce at point P that is in the center of the square.

b) If an electron is released from rest at P, what are the magnitude and direction of the net force and its acceleration that these wires exert on it?

6. Charges is distributed uniformly along a semicircular rod of radius r = 5.0 cm such that half of the semicircle is charge with Q₊ and the other half is charge with Q_-, as shown below. If the charge is Q₊ =10.0 µC and Q_- = -10.0 µC, find the electric field at point P, the center of the semicircle.

7. Two point-charges q₁ and q₂ are held in place 4.50 cm apart. Another point charge Q = -1.75 μC of mass 5.00 g is initially located 3.00 cm from q₁ and q₂ as shown in the figure below. When Q is released from rest you observe that the initial acceleration of Q is 324 m/s² upward, parallel to the line connecting the two point charges q₁ and q₂. Determine the amount of charge for q₁ and q₂.

8. Eight charges of magnitude Q = 1.25 µC are located at the corners of a cube of side L = 0.5 nm as shown in the figure below. One corner is at the origin and the edges lie along the rectangular axes. Find the net force on the charge located at the position vector r‾  = Lxˆ + Lyˆ  + Lzˆ given that the nearest neighbor of any charge has the opposite sign.