# Physics 102 - Electrostatics

Lightning strikes Earth an average of 100 times per second

Electrostatics

Now we start into the study of electromagnetism, beginning with electrostatics or electricity at rest. We will cover topic such as electrical force, charge and the electric field. Electricity is everywhere, from the skies to the neurons in our brains. Let's begin at the beginning...

Electrical charge

Particles come in three charge types: positively charged, negatively charged and neutral. These particles feel forces from each other depending on the charges. Neutral particles are neither electrically attracted or repelled by positive or negatively charged particles. This is why most neutrinos can pass through the entire Earth without being deflected. For positive and negatively charged particles, like charges repel each other and opposite charges attract each other.

Charging by friction

A wool carpet has a stronger attraction for electrons than do leather soled shoes so the electrons are stolen from the shoes by the carpet, leaving a person with a deficit of electrons or a positive charge. If you then touch a doorknob, electrons in the doorknob are attracted to your finger, causing a small shock. If the shoes are made of rubber, they will steal electrons from the carpet. This will also cause a shock, except that this time the extra electrons will jump from your finger onto the doorknob.

balloon demo

Van de Graff generator demo

electroscope demo

Charging by induction

Charges can be made to move even if objects don't actually touch each other. For example, a negatively charged wand will cause electrons on a metal sphere to move away, leaving a positive charge close to the wand.

If the metal sphere is grounded while the wand induces a charge, the electrons will flow away to ground and leave the sphere with a net positive charge.

Charge is measured in units called Coulombs. It is a conserved quantity - charge cannot be created or destroyed. An electron is a fundamental particle that carries a charge of -1.6x10-19Coulombs. Protons are particles made up of quarks. Each proton carries a charge equal and opposite in sign to that of an electron.

The electric force between two charged particles is described by Coulomb's law. The signs of the two charges will determine the direction of the force.

The gravitational force between two particles with mass is described by a similar equation. Notice the gravitational force is always attractive.

Coulomb's law and the gravitational force equation are two examples of inverse square laws.

Inverse square laws describe forces which emanate from a point source.

electric field hockey

Electrical charge and atoms

Atoms are made of nuclei (protons and neutrons) surrounded by a cloud of electrons. Most atoms are electrically neutral - that is, the charges of the protons in the nuclei are exactly balanced by the charges of the surrounding electrons. If an atom loses or gains one or more electrons, it has a net nonzero charge and is called an ion.

An early model of the atom was similar to that of the solar system, with electrons orbiting the nucleus as planets orbit the sun. There are fundamental differences between the way planets act in a gravity field and the way electrons act in the electrical field of the nuclei. For one thing, an electron is not localized in the same way that a planet is. It resides in a cloud like state.

Also, a planet could take any orbit around the sun, given the right velocity. Electrons do not have that freedom. They can only reside in very specific quantized energy states called orbitals.

Charge separation

An atom can become electrically polarized if a nearby charge causes its electron cloud to become distorted.

Charge separation in atoms can be a wide scale effect.

Electric field

It is convenient to talk about the electric force on a small test charge. We define the electric field to be the force per charge.

We can map out the electric field by placing tiny arrows showing which way it points. It tends to form lines, which are called electric field lines.

It is fairly intuitive, by looking at the patterns of the field lines of two charged particles, whether they are attractive or repulsive. Also, where the force is stronger, the field lines are closer together.

electric field applet

Electric potential

Potential energy is relatively easier to grasp in terms of gravitational potential energy. The gravitational force on an object is what we call its weight. It is mathematically defined as its mass times the acceleration due to gravity, or F = mg. Work is defined as a force times the distance it has been displaced, or W = Fd. If I am lifting an object, the work I do against gravity is W = mgh, where h is the height.

By lifting the object, I have increased its potential energy. This energy will be converted to kinetic energy if I drop the object. In other words, it will move faster and faster as it falls to the ground. The energy of motion is called kinetic energy. The higher I lift it, the faster it will move before it hits the ground. The more potential energy I give it, the more energy it has to convert to kinetic energy. Energy is conserved. It is not created of destroyed, only converted from one form to another.

We can also do work using charged objects. Two oppositely charged particles are attracted to each other. If I pull them apart, I have done work on them. If I let them go, they will "fall" back toward each other, converting the potential energy to kinetic energy of motion. With charged particles, I can also do work by pushing like charges together. If I let them go, they will push apart from each other, again converting potential energy to kinetic energy.

Electric potential is defined as the electric potential energy per unit charge. The units of electric potential are, therefore, Joules/Coulomb. We define Joules/Coulomb as Volts.

We can also measure the electric potential at every point in space. It doesn't have a direction associated with it like a force does, so we don't use arrows to describe it.

electric field applet

Capacitors

If I do work to separate charges (using a battery, for example) I can store the separated charges on metal plates. This configuration is called a capacitor. Early capacitors were called Leyden jars. They used sheets of foil rolled up with a layer of insulator to store separated charges.

We use capacitors to deliver an electric shock to restart a heart with a defibrillator.

When the EMT or doctor says "Charging!" They are charging the capacitor.

Conceptual questions

1) Why do clothes often cling together after tumbling in a clothes dryer?

2) At some automobile toll-collecting stations, a thin metal wire sticks up from the road and makes contact with cars before they reach the toll collector. What is the purpose of this wire?

3)An electroscope is a simple device consisting of a metal ball that is attached by a conductor to two thin leaves of metal foil protected from air disturbances in a jar, as shown. When the ball is touched by a charged body, the leaves that normally hang straight down spread apart. Why? (Electroscopes are useful not only as charge detectors, but also for measuring the quantity of charge: the more charge transferred to the ball, the more the leaves diverge.)

4) Is it necessary for a charged body to actually touch the ball of the electroscope for the leaves to diverge?

5) The five thousand billion, billion freely moving electrons in a penny repel one another. Why don't they fly out of the penny?

6) How does the magnitude of electric force compare between a pair of charged particles when they are brought to half their original distance of separation? To one-quarter their original distance? To four times their original distance? (What law guides your answers?)

7) The proportionality constant k in Coulomb's Law is huge in ordinary units, whereas the proportionality constant G in Newton's law of gravitation is tiny. What does this indicate about the relative strengths of these two forces?

8) If you rub an inflated balloon against your hair and place it against a door, by what mechanism does it stick? Explain.

9) How can a charged atom (an ion) attract a neutral atom?

10) If you place a free electron and a free proton in the same electric field, how will the forces acting on them compare? Their accelerations? Their directions of travel?

11) Suppose that a metal file cabinet is charged. How will the charge concentration at the corners of the cabinet compare with the charge concentration on the flat parts of the cabinet?