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.
2.1: Introduction to Electricity
As you know, the atoms that make up physical objects include protons, electrons, and neutrons. Protons are positively charged, electrons are negatively charged, and neutrons are neutral. Consequently, all things are made up of charges.
Opposite charges attract one another (negative to positive). Like charges repel one another (positive to positive or negative to negative). Most of the time, positive and negative charges are balanced in an object, making that object neutral.
Static electricity results from an imbalance between the negative and positive charges in an object. These charges can build up on the surface of an object until they find a way to be released or discharged. One way to discharge them is through a circuit.
2.2: Conductors and Insulators
A conductor is a material that allows electrons to flow freely through them from particle to particle. The moving electrons may lose some energy when they collide with the fixed atoms and molecules, but they can move in a conductor. Superconductors allow the movement of charge without any loss of energy. For example, electric current can flow freely through a conductor. Examples of conductors include metals such as aluminum, copper, gold, iron, silver, and steel. Salty water and molten salt are also conductors.
Insulators, in contrast, are made from materials that lack conduction electrons. The electrons and ions in insulators are bound in the structure and cannot move easily. The charge moves with great difficulty, if at all. Examples of insulators include most non-metallic solids, such as amber, fur, glass, plastic, porcelain, rubber, wood, and most semi-precious gems. Pure water and dry table salt are also good insulators.
2.3: Coulomb's Law
We can detect the presence of an electric charge by the forces they exert on other charged objects. We call these forces electric forces. These forces depend on how far away you are, just like the gravitational force between two planets depends on their separation. Like the law of universal gravitation that Newton used to explain how planets move around the Sun, there is also a force law of electricity that explains how electrons are held by the nucleus inside an atom (even though that requires additional ingredients from the modern theory of quantum physics).
The strength of the electric force between two charged spheres depends on their separation in the same way as the gravitational force between two spheres: an inverse-square law. This means that if you double the distance, the force decreases by a factor of four. The mathematical formula for electrostatic force is named after the French physicist Charles Coulomb (1736–1806), who performed experiments and first proposed a formula to calculate it.
2.4: Electric Field and Gauss' Law
When Newton chronicled the law of universal gravitation, he also explained the well-known observation that all objects fall at the same acceleration on Earth's surface. Without going into the details, the crucial fact in the explanation was that the gravitational force on any test object is proportional to the mass of the test object.
Therefore, when the gravitational force is divided by the mass of the test object, you get a quantity that is independent of the test object itself. For gravity, that is just the universal value of acceleration. It only depends on the properties of the other object involved in the gravitational pull: the Earth.
2.5. Applications of Electrostatics
Electrostatics (also known as static electricity) is the branch of physics that deals with stationary electric charges. This means it involves charges whose distribution in space stays constant over time. Although Coulomb's Law is the foundation of electrostatics, it is not always easy to apply when large numbers of charged particles are involved.
Using field lines as a tool, we can draw conclusions about an electric field even when the charges are crowded so densely that they lose their individual identity. This happens when charges are transferred to a conductor. We approach this situation from what we know about the electric field itself, rather than from the individual charges, as the cause of the electric field. We can do this with the help of some additional assumptions. The main assumption is that in an electrical conductor in electrostatic equilibrium, charges will arrange themselves on the surface so that their resultant electric field lines point exactly perpendicular to the surface.
2.6: Electric Potential and Electric Potential Energy
Electric potential energy refers to the energy something has due to its position in an electric field (the capacity for doing work due to its position or configuration). For example, if you have a positive charge (+ charge) and you move it near another positive charge, it will want to deflect. If you push it closer to the positive charge, it will want to deflect more. When the charged object is let go from rest, it will speed up and gain kinetic energy by an amount equal to the change in its electrical potential energy. As for all forms of energy, the standard unit of electrical potential energy is the Joule.
Any test object can have an electric potential energy only if it feels an electric force. Recall that the electric force on a test object is proportional to its charge. This makes the electric potential energy proportional to the charge, too! Therefore, one can play the same game with the potential energy that led us from the electric force to the electric field: divide by the charge to get a quantity that is independent of the test object.
The result is the electric potential. It is to the electric potential energy what the electric field is to the electric force. In other words, electric potential is the would-be electric potential energy. Similar to the electric field, the electric potential depends on the distribution of all the charges that are present before we decide to introduce an additional test charge to probe what those existing charges would do to it.
As with any form of potential energy, you have to choose a reference point to specify its value. The choice of reference point is completely arbitrary because only changes in electrical potential have any physical significance. The change in electric potential between two points is also called the voltage between those points.
2.7: Capacitors and Capacitance – Storage of Electric Energy
A capacitor (also called a condenser) is a device that stores electric charge in an electric field. It is a passive electronic component with two terminals. Although they work in different ways, a capacitor looks like a battery, which also stores electrical energy. Inside the capacitor, the terminals connect to two metal plates separated by a non-conducting substance, or dielectric.
The dielectric dictates what kind of capacitor it is and for what it is best suited. Depending on the size and type of dielectric, some capacitors are better for high frequency uses; others are better for high voltage applications.