### Unit 2: Electrostatics

Now, let's turn to the study of electricity and magnetism, two different aspects of electromagnetism. We start by looking at electrostatics: the rules that govern the behavior of static charges. Thales of Miletus (c. 624–548 bc), the Greek mathematician, astronomer, and philosopher, carried out the first experiments on electrical phenomena when he observed that you can generate a static charge when you rub amber with wool.

**Completing this unit should take you approximately 20 hours.**

Upon successful completion of this unit, you will be able to:

- state Coulomb's law and identify the units of the physical quantities contained in the law;
- solve problems involving electric forces, electric fields, and electric potentials;
- explain Gauss' law in words;
- compare and contrast the electric potential and the electric field;
- solve problems using Gauss' Law;
- solve problems involving the motion of charged particles in an electric field;
- define capacitance and describe the factors that determine capacitance;
- describe the effect of a dielectric material in a capacitor; and
- define electric potential energy and describe how capacitors can be used to store energy.

### 2.1: Introduction to Electricity

Watch this lecture series.

Read "Chapter 21: Electricity and Circuits" on pages 561–565. Complete the self-checks (answers on page 1010). Think about the discussion questions and examples, and solve problems 1–9 on pages 601–602. You can check some of the answers here.

Read "Chapter 26: The Atom and E=mc

^{2}" on pages 731–742. Answer the self-check questions (answers on page 1011). Think carefully about the Millikan's Fraud discussion, which illuminates the basis of science and how it is eventually self-correcting. Think about the discussion questions and examples, and solve problems 2 and 4 on page 787. You can check your answer to problem 4 here.Read this chapter. Try each of the problems in it before looking at the solutions. Make sure you understand how to approach solving the problem so that you can obtain the solution yourself.

This demonstration illustrates the relationship between the charge on the two balls and the separation between them. Use this worksheet to work out this relationship by considering the balance of the forces acting on the charged balls.

This demonstration illustrates how a Van de Graaff generator generates static charges and collects the charges on a metal sphere. The voltage on the sphere is proportional to the amount of charge collected. Though it appears that the collected charge on the sphere would increase indefinitely, in reality, paths for loss of the collected charge exist and typically limit the static voltage on the sphere to a fraction of a megavolt, although Van de Graaff generators specialized for use in nuclear accelerators can generate 10 megavolts or more.

### 2.2: Electric Field and Gauss' Law

Read "Chapter 22: The Nonmechanical Universe" on pages 618–630. Answer the self-check questions (answers on page 1010). Think about the discussion questions and examples, and solve problems 1–7 and 10 on pages 644–645. You can check some of your answers here.

Watch this lecture series.

Watch this lecture. Check your understanding by attempting this problem set. Solutions can be found here.

Read this chapter and try example 4.1 before looking at the solution.

This demonstration illustrates the effect that a uniform electric field has on the motion of an electric charge. Why do the charges follow a parabolic path? Think of an analogy that describes the effects of gravity on a projectile.

### 2.3: Electric Potential and Electric Potential Energy

Watch this lecture.

Please click on the link above, and read this chapter after viewing the lectures above. Try all four worked examples before looking at the solutions. Make sure you understand not only the solutions but also how to approach solving the problem so that you can obtain the solution yourself. You will be responsible for being able to solve problems of this type on the final exam.

This demonstration illustrates what you would find in a lab experiment where two electrically charged bodies are placed on a table, and you measure the electric potential (roughly speaking, the voltage relative to a reference point) as a function of position on the table. The electric potential is displayed as a series of equipotential curves, or curves along which the electric potential is constant. Vary the position and strength of the charges, and then view the results with both the 3D and the contour plot. Turn on the field direction, and notice that the electric field is everywhere perpendicular to the equipotential curves. This is because the electric field is proportional to the gradient of the electric potential.

This demonstration is an extension of the previous demonstration on Electric Dipole Potential. Shown here again is an electrostatic dipole where the strengths of the electric charges can be varied. The graph shows the lines of an electric field. The lines of an electric field are everywhere perpendicular to the equipotential curves. Note that this does not mean that the

*magnitude*of the electric field is constant along an electric field line; it only means that the magnitude of the electric field points along that line. Vary the two charges' positions and magnitude to gain some feel for how the electric field behaves. The calculations required by the demonstration are complex, so wait between changes for the graph to once again become smooth.

### 2.4: Capacitors and Capacitance – Storage of Electric Energy

Watch this lecture series.

Please read this chapter. There are 4 worked examples in the chapter. Try each of these problems before looking at the solutions. Make sure you understand not only the solutions but how to approach solving the problems so that you can obtain the solutions yourself. You will be responsible for being able to solve problems of this type on the final exam.

This demonstration can be treated as a combination laboratory project and homework problem. The capacitance of a parallel plate capacitor depends on the area and separation of the plates and the dielectric constant of the material between them. In this demonstration, you will control the geometry and materials of the capacitor, and you will measure the charge resident on the capacitor as a function of applied voltage. First, keep the voltage fixed, and set the values for the area of the plates, plate separation, and the dielectric constant. Calculate the capacitance using the formula given in the demonstration or the reading resources, and confirm that you get the same result as the program (pay attention to the units of all physical quantities!) Then, use the values of the voltage and the capacitance to calculate the charge on the capacitor. Again, confirm that your result is the same as that in the demonstration.

This demonstration, again, can be used as an interactive homework problem. A partially-filled capacitor can be viewed as a pair of capacitors, one filled and the other unfilled. (Note that this is only true for geometries where the dielectric interface is approximately on an equipotential surface, as nothing then changes when the extra pair of metal plates is inserted. This same technique could be used on a partially-filled cylindrical or spherical capacitor, for example, provided the dielectric surface was cylindrical or spherical, respectively.) Use the formula for the capacitance in terms of the area of the plates, the distance between the plates, and the dielectric constant to write down the capacitance of the "filled" and "empty" capacitors. Notice that the distance between the plates of each capacitor depends on the percentage k of the dielectric material, as shown in the demonstration. Then, use the formula for the equivalent capacitance of the two capacitors connected in series to derive the result in the "Details" section of the demonstration. The values of A and d is fixed and given in the "Details" section of the demonstration. You can select a value of k and a dielectric material (you will have to look up the value of the dielectric constant), and calculate the capacitance of the partially filled capacitor. Again, confirm that your result agrees with the demonstration.

This demonstration provides examples for both capacitors and inductors, but for now, work only with the capacitors. Treat this demonstration as a laboratory experiment in which you measure the capacitance of various geometries and use theory to confirm that the capacitances are correct. Then, determine the electromagnetic field energy driven by applied voltage from the demonstration. First, calculate the charge on the capacitor's plates, and the resultant electric field between the plates. Use the formulas given in the description in the demonstration, or the readings above, and confirm your result. Then, calculate the electric energy stored in the capacitor, and the electric energy density. Again, confirm your result.

### Unit 2 Assessment

Take this assessment to see how well you understood this unit.

- This assessment
**does not count towards your grade**. It is just for practice! - You will see the correct answers when you submit your answers. Use this to help you study for the final exam!
- You can take this assessment as many times as you want, whenever you want.

- This assessment