1. When a positively charged rod is brought close to an electroscope that has been charged negatively, the leaves fall together. But if it is brought even nearer, the leaves spread apart again. Explain what's happening, use appropriate diagrams.

2. In each diagram below, draw a vector showing each force vector and the net force on the round particle due to all the square fixed charges.

3. a. In the diagram, a rubber rod is given a charge Q distributed uniformly over it by rubbing it with fur. It is noticed that when an uncharged metal ball is suspended by a string at a particular location near the end of the rod is drawn toward the rod by some mysterious force. Show the distribution of charges on both the rod and the ball and explain why this occurs.

3 b. When the rubber rod is removed, and replaced by a metal rod of the same length which has been given the same amount of charge, it is found to cause the ball to come much closer. Show the distribution of charges on both the rod and the ball and explain why this occurs.

4. Find the net force on the -1C charged object due to the other charges in the diagram below.

5. A student has said that the electric field inside a charged sphere is always zero.
Place the single word at the proper location in this sentence to make it true.

6. Find the electric field in component form at the position of the 4C charge. Also find its magnitude and direction.

7. What you see in the figure below is a cut-away view of a hollow metal sphere. The gray area indicates solid metal. The white region in the center indicates the hollow center, in which has been placed, some magical how, a charge Q3 = +4C. Then a bucket containing +5 C of charge is dumped onto the outer surface of the metal sphere.

Your task is to determine the electric field at the locations A = 1 m from the center, B = 2m from the center, C = 3 m from the center, and D = 4m from the center , and the charge Q1 on the outside surface of the hollow metal sphere, and the charge Q2 on the inside surface of the hollow metal sphere.

8. An electron is observed to accelerate northward with an acceleration of 1.6x1016 m/s2. (mass of an electron is 9x10 -31 kg, charge is 1.6x10-19C.) Find the direction and magnitude of the electric field at this location.

9. Consider a thin plastic rod bent into an arc of radius R and angle f. The rod carries a uniformly distributed positive charge Q. Follow the steps below to obtain the components Ex and Ey of the electric field at the origin,due to the rod?

a) Use a diagram to explain how you plan to cut up the charged rod, and draw the DE contributed by a representative piece.
b) Express algebraically the contribution each piece makes to the x and y components of the electric field . Be sure to show your incremental component dE of the electric field on your drawing. (Recall that the arc length Ds of a circular arc of radius R , subtended by an angle of Du, is R Du.)
c) Write the summation as an integral for each component of E, and simplify the integral as much as possible. State explicitly what the range of your integration variable is.
d) Evaluate the integrals to find Ex and Ey.