Physlets run in a Java-enabled browser, except Chrome, on the latest Windows & Mac operating systems. If Physlets do not run, click here for help updating Java & setting Java security.

# Physlet^{®} Physics 2E: Electromagnetism

## Chapter 22: Electrostatics

The charge that an object carries is as fundamental as the mass of that object. It may, in fact, be more fundamental. Although Albert Einstein predicted, and experiment later confirmed, that mass can be converted into energy and thus is not strictly conserved, physicists have never observed an event that did not conserve charge. The theory that predicts electrostatic (and electrodynamic) interactions is one of the most accurate and successful theories ever developed. Although it seems that charge may appear and disappear in everyday experiments, what you are actually observing is only the rearranging of existing charges. Whenever charge appears on an object, another object picks up an equal charge of the opposite sign. Whenever charge disappears, you are recombining charges of opposite sign.

## Chapter 23: Electric Fields

In the previous chapter you explored Coulomb's law, the law that describes the force between charges. In this chapter, we describe what happens to the space around an electric charge; specifically, that an electric field is created. The field approach allows us to describe the force a charged particle experiences as due to the presence of the electric field created by nearby charges. Operationally, an electric field is simply a description of the force (magnitude and direction) a positively charged object would experience divided by its charge (**E** = **F**/q). In the process of representing this vector field, we will use field vectors, field lines and "test charges" (charges that only feel the force due to other charges, but do not change the external electric field).

## Chapter 24: Gauss's Law

Electric fields decrease with distance from their source as 1/r^{2}. Compare the surface area of a cubic box with sides of length r with a sphere of radius r. Their surface areas are 6r^{2} and 4πr^{2}, respectively. Although the constants differ, each surface area increases by r^{2} as the size of the object increases. The observation that the field strength decreases in the same proportion as the area increases leads to Gauss's law. Nineteenth century physicists were fond of analogies between fields and fluid flow. If fluid flows from a source, then the amount of fluid flowing through any surface that encloses that source must be constant regardless of the shape of that surface. The amount of fluid passing through a surface is sometimes called the flux. Although it would be incorrect to think of electric and gravitational fields as fluids, the mathematical machinery is identical and we will need to calculate a quantity known as the electric flux that is the product of the field strength and surface area.

## Chapter 25: Electric Potential

In mechanics there were two basic ways to approach problems, from the point of view of forces or energy. The same is true in electrostatics, but instead of forces and potential energy, we generally use electric fields (force/charge) and electric potentials (potential energy/charge). As before, the change in a potential energy is the negative of the work required to move an object (in this case a charged object). Instead of an electric field (a vector), we talk about the electric potential (a scalar). The electric potential is measured in Volts and, as with potential energy, the point of zero electric potential is arbitrary. Common conventions are to call Earth (and any conductors connected to Earth) zero Volts or to set the zero of electric potential at a distance very far away (infinity) from the charge distribution.

## Chapter 26: Capacitance and Dielectrics

Now that you have developed an understanding of electric fields and electric potentials, you have the tools needed to understand a capacitor. A parallel-plate capacitor consists of two conducting sheets close enough together so that they can store equal and opposite charge with a potential difference between them. The amount of charge a parallel-plate capacitor stores at a particular voltage depends on its geometry and is characterized as its capacity or *capacitance* (measured in farads = 1 coulomb/volt). A common way to increase the capacitance of a capacitor is to put a dielectric (non-conductor) between the conducting plates. The charges in the dielectric are bound charges (not free to move away from a particular site within the material) in comparison with the free electrons of a conductor (that move in the presence of an electric field).

## Chapter 27: Magnetic Fields and Forces

Currents (moving charges) create magnetic fields. The familiar refrigerator magnetic has moving charges that create its magnetic field (electrons orbiting the nucleus of the atom), but we don't have a complete understanding of why different materials have different magnetic properties. In this chapter we won't worry about what creates the magnetic field and will focus instead on i.) describing magnetic fields (with field vectors, a compass, and field lines) and ii.) the effect of magnetic fields on charged particles (the Lorentz force). We will map magnetic field lines because that tells us about the forces between magnets (that like poles repel). Further, we will explore the force that a charged particle experiences in a magnetic field. This force depends not only on the magnitude of the magnetic field, but on the speed of the particle as well as its orientation in the magnetic field.

## Chapter 28: Ampere's Law

In the previous chapter, we mapped magnetic fields and explored the force of magnetic fields on moving charges and currents. In this chapter, we will focus on the cause of magnetic fields (moving charges) and how to calculate fields created by current carrying wires. We will use Ampere's law to calculate the magnetic field and use right-hand rules to predict the direction of the magnetic field from an assembly of current carrying wires. As with Gauss's law, to use Ampere's law we depend on the symmetry of the configuration to make the needed simplifications to the calculations. Once we have expressions for fields from current carrying wires, we can investigate interactions between wires. Since a current carrying wire creates a magnetic field, it can exert a force (Lorentz force: **F **= q** v **x** B **= I** L **x** B**) on the current carriers in a nearby wire.

## Chapter 29: Faraday's Law

Moving charges create a magnetic field (think of current in a wire). Do changing magnetic fields create an electric field? The answer is yes and Faraday's law describes exactly what happens. A changing magnetic field induces a current in a conductor. Similarly, if a conductor moves in and out of the field, the same effect and is described by Faraday's law: a changing magnetic flux (magnetic field times cross-sectional area) induces an emf (a voltage) which causes a current in a closed loop. Lenz's law (which is part of Faraday's law) tells you that the induced current flows in a direction to oppose the change in flux.