Instructor: K. W. Nicholson

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

2. An electron is observed to accelerate northward with an acceleration of 1.6 x 106 m / s2. (Electron mass = 9x10-31kg, charge is -e, where e = 1.6x10-19C.) Explain how to use the definition of electric field to determine the electric field at this location, and give the direction and magnitude of the field.

3. Find the x and y components of the electric force on Q1 exerted by the other two charges.

4. Here is a view from above of a portion of a circuit containing three identical light bulbs (the rest of the circuit including the batteries is not shown).

(a) The compass is placed on top of the wire, and it deflects 20 degrees away from north as shown (the wire is underneath the compass). What direction are the electrons moving at location Pl ? How do you know?

b) In the steady state, 3 x 108 electrons pass location Pl every second. How many electrons pass location P2 every second? Explain briefly.

(e) Describe the relative brightness of bulbs Bl, B2, and B3. Explain briefly.

5. Here is a circuit consisting of two flashlight batteries, a large air-gap capacitor, a nichrome wire, and thick copper wires. The circuit is allowed to run long enough that the capacitor is fully charged with +Q and -Q on the plates.

Next you pull the two plates further apart. Describe what happens, and explain why in terms of the fundamental concepts of charge and field (do not use "potential" or "capacitance"). Include diagrams.

6. Here are three circuits labeled A, B, and C. All the long bulbs, capacitors, and batteries are identical, and are like the equipment you used in class. The capacitors are initially uncharged. In each circuit the batteries are connected for a short time T and then disconnected. The time T is only twenty percent of the total charging time through a single long bulb, so that the bulb brightness doesn't change much during the time T.

(a) In which circuit (A, B, or C) does the capacitor now have the most charge? Explain.

(b) In which circuit (A, B, or C) does the capacitor now have the least charge? Explain.

7. A solid metal sphere of radius r1 has a charge +Q. It is surrounded by a concentric spherical metal shell with inner radius r2 and outer radius r3, that has a charge -Q on its inner surface and +Q on its outer surface. In the diagram, point A is located at a distance r4 from the center of the spheres. Points B and C are inside the metal shell, very near the outer and inner surfaces respectively. Point E is just inside the surface of the solid sphere. Point D is halfway between C and E. Point F is a distance r1/2 from the center.

(a) Is each of the following potential differences > 0, = 0, or < 0? Briefly explain why in terms of electric field.

VB - VA;

VC - VB;

VD - VC;

VF - VE

(b) Calculate the potential relative to infinity at point F ( VF - V° ). Explain your work.

8. The quantity of charge q (in C) passing thru a surface of area 2 cm2 varies with time as q = 4t3 + 5t +6, where t is in seconds. What is the instantaneous current thru the surface at t = 2 s ?

9. Find the total resistance between the points A and B of the configuration below.

10. a. Find the system of equations that will obtain current in each of the resistors in the figure below.

10b. Solve the system of equations above.

10 Pt Bonus

In the figure at right, find the total capacitance between :

a) A and C

b) A and B