Electrostatics

the study of electrical charges at rest

A charged object is created by the separation of charges:

• an atom is electrically neutral; it has the same number of protons (positive charges) as it does electrons (negative charges)
• objects are charged by adding or removing electrons
• a positive charge occurs when there are fewer electrons than protons; its classical definition is the charge accumulated by a glass rod rubbed with silk or wool
• a negative charge occurs when there are more electrons than protons; its classical definition is the charge accumulated by a hard, rubber rod rubbed with fur

The choice of which name went with which charge was arbitrary. We follow the convention today that was set by Benjamin Franklin. Franklin called the charge accumulated by the rubbed glass rod to be positive and that on the rubber rod negative. Franklin also argued that whenever a certain amount of charge was produced on one body in a process, an equal amount of the opposite charge was produced on another body. In any process, the net change in the amount of charge produced is zero.

Law of Conservation of Electric Charge The net amount of electric charge produced in any process is zero. If one region or object acquires a positive charge, then an equal amount of negative charge will be found in neighboring regions or objects.

During the last century, it became clear that electricity begins inside the atom itself. In a simplified view, the postivively charged nucleus (containing postively charged protons) of the atom is surrounded by negatively charged electrons. Neutral atoms contain equal amounts of protons and electrons. If an electron is gained or lost, the atom is now either negatively or positively charged and is called an ion.

When objects are charged by rubbing, the electrons (which are free to move) are transferred from one object to another. For example, if a plastic ruler is rubbed with a paper towel, the plastic ruler becomes negatively charged because electrons are transferred from the towel to the plastic ruler. Eventually, this charged is lost, leaking off onto water molecules in the air. Water molecules are polar (though neutral, their charge is not distributed uniformly).

Electrostatics Lab Activities

Conductor

a substance that allows electrons to move easily throughout

Insulator

a substance that does not allow electrons to move freely; electrons stay in one place

An Animation Showing the Difference Between Conductors and Insulators

Semiconductor

partially conductive, partially insulative

Electroscope

an instrument used to detect the presence of an electrostatic charge

Coulomb ( C )

the SI unit of charge 1 C = 6.24 x 10¹⁸ electrons

There are two kinds of electrical charges, positive (+) and negative (-). Like charges repel and unlike charges attract. Thus, electrical charges exert a force on other electrical charges. This electrostatic force is directly proportional to the product of the charges and inversely proportional to the square of their distance of separation (another inverse square law relationship!)

Methods of charging an object:

1. Conduction
   a charged object touches another object; the amount of charge equally divides between the two objects; the same sign charge is acquired by each object

   Induction

   a charged object is brought near, but not touching, another object; it attracts charges opposite to it and repels charges like it; when a ground is used, the opposite charge is acquired on the other object; it is thus charged without being touched. Of course, the net charge is still zero. Charges have merely been separated.

Charging by Induction animation

Electroscope Device used to detect charge.

Coulomb’s Law describes the electrostatic force between two charged objects. Charles Coulomb used a torsion balance in the 1780's to investigate electrical forces. He found that if the charge is doubled on a charged object, the electric force it exerts on another charged object is also doubled. He found that if the distance between two charged objects was allowed to increase, the electric force between them decreased with the square of the distance between them.

where k is Coulomb’s constant, or k = 9 x 10⁹ Nm²/C² (approximate value) or k = 8.988 x 10⁹ Nm²/C² (actual value)
q is the magnitude (NO sign) of each charge in coulombs
d is the distance of separation in meters
F is the electrostatic force in Newtons. It is either attractive or repulsive.

Coulomb's Law Explanation

Permittivity of free spaceCoulomb's constant, k, is often written in terms of e_o, the permittivity of free space.
k = 1 / (4 p e_o)

Coulomb's law calculates the magnitude of the electric force between two charged objects, when the charges are known. The direction of the force is always along a line joining the two objects. If the two objects have the same sign, the force on either object is directed away from each other. If the two objects have opposite signs, the force on either object is directed toward each other.

(Note the similarity between Coulomb's law and the law of universal gravitation. Both are inverse square laws-the force is proportional to the inverse square of the distance. Both are proportional to the product of a property of each body-mass for gravity and charge for electricity. Gravity is always an attractive force; the electric force can be attractive or repulsive.)

Since charges are small, they are usually expressed in non-SI units of microcoulombs, nanocoulombs, or picocoulombs. They must be converted into Coulombs for calculations.
1 mC = 1 x 10^-6C
1 nC = 1 x 10^-9 C
1 pC = 1 x 10^-12C

Elementary charge (q_o)

the charge of either an electron or a proton. The charge of a proton is equal in magnitude to that of an electron, but it positive.
q_o = 1.6 x 10^-19 C

1. Always remember to convert everything to SI units! A mC is not an SI unit. It must be converted into Coulombs. Remember to convert distances in centimeters to meters.
2. Forces are vector quantities. We will use Coulomb's law to calculate the magnitude of the electrostatic force between two charges. When we are calculating magnitude, we will not consider the signs of the charges.
3. Forces are vector quantities. We will use free body diagrams to determine the direction of the electrostatic force between two charges.

   
   

   Determine the magnitude of the electrostatic force exerted by the +4 C charge on the +6 C charge. It is repulsive or left.

   What is the resultant force on the middle charge?

   
   

   Determine the magnitude of the force exerted on the +4 C charge by the +5 C charge. Its direction is right (repulsive). Determine the magntitude of the force exerted on the +4 C charge by the +6 C charge. Its direction is left (repulsive). Use positive and negative signs to represent the directions of the forces. Assign a negative sign to force acting to the left and a positive sign to the force acting to the right. The resultant force on the +4 C charge is the sum of these forces.

AP Multiple Choice questions

1. You may be asked to predict the remaining charge when unlike charged spheres are touched and then separated.
2. You may be asked to predict the magnitude and direction of the electrostatic force acting between charges.
3. You may be asked to predict the new force between two charged objects if the distance and/or the charges are changed.

AP Free Response questions

1. A very common problem is one in which a charge (or two charges) are hanging from a thread (or threads). (If it's one charge, it is usually in an electric field). You will be asked to draw a free body diagram showing all the forces acting on the charge.
2. In the same type of problem, you may be asked to calculate the magnitude of the charge, the distance of separation, the magnitude of the force on the charge, and/or the tension in the string. (Important mathematical relationship to remember: tan Q = sin Q divided by cos Q.
3. In the same type of problem, they combine mechanics concepts by asking you to answer several different types of questions if the string is cut. You might be asked to calculate the resulting acceleration of the charge (remember, gravity is accelerating it vertically and the force due to the electrostatic repulsion or electric field is accelerating it horizontally). You might be asked to calculate a time for it to travel a known distance or to calculate how fast it is going at the end of a known distance (both of these require you to know the acceleration).

How a Van de Graff Generator Works

The Proton Gun Interactive Lab

An Explanation for Lightening

Electrostatics Sample Problems

Electrostatics Homework

AP Electric Forces & Fields Class Problems

AP Objectives-Electric Field

Class Electrostatics Activity