We all have experienced a situation where we are suddenly shocked while touching an object (such as a door knob, desk, etc.). What is the cause of this sudden electric discharge? It happens to be related to the topic of static electricity, the most common example is pictured below. However, there are multiple components that go into answering this question, and these will be explained throughout this chapter summary.
Van de Graaff Generator producing static electricity
Static electricity

Particles and Charges
All matter is made up of atoms, which in turn are made up of protons, neutrons and electrons. Protons and neutrons are made up of quarks, while the electron is considered an elementary particle, as it is not made up of anything else. Classically, thanks to Benjamin Franklin's arbitrary choice, electrons have a negative electric charge (-), protons have a positive electric charge (+), and neutrons do not have a charge. Since atoms are made of these particles, and all matter is made of atoms, everything is filled with tiny electrical charges. The balance of the negative and positive charges creates an electrically neutral object (wood, plastic, etc) when not interacting with another object. Anything with charge can interact with anything charged (or not charged) through electromagnetic force. Each charged particle emits an electric field, and (if in motion) can create a magnetic field as well. Both of these forces can act upon other objects to create a repulsive or attractive force.

When two positively or negatively charged objects (atoms for example) come within range of each other they will repel, while a positive and a negative charge will attract to each other. This is simply demonstrated with two magnets, if the positive and negative sides are placed near each other, they will attract and come together, however if one of the magnets is turned around then they will repel from each other and it will be difficult to get them together. In addition to this, a positive (or negative) charge in contact with a neutrally charged object will have an attractive force as well. This is due to an induced charge, which means that when a charged object is put near an uncharged objects, the electrons in the uncharged object will maneuver around to be either closer to or farther away from the charged object (depending on its charge). This is depicted in the diagram below.
Induced charge
Induced Charge
The white block (B) was originally neutrally charged, but when the grey positively charged object (A) comes close, the electrons try to get towards that object, thus creating charge separation.

Coulomb's Law
The electrostatic force between charged particles can be calculated through Coulombs Law. Mathematically, it is defined as:
Coulomb's Law
where q is the charge of particle one and two (in coulombs), r is the distance between them (in meters) and k is a proportionality constant (8.99 x 10^9 N m^2 C^-2) which is also defined as:
Permittivity constant
where ε0 is the permittivity constant.

This situation is depicted through the following diagram, showing the two charges (q1 and q2) along with the distance (r)
Two charges separated by distance r
Coulomb's Law diagram
You may recognize the similarities between Coulombs Law and Newton’s Law of Gravity:
Newton’s Law of Gravity
where G is the gravitational constant (6.674 x 10^-11 m^3 kg^-1 s^-2), m is the mass of the two objects (in kg) and r is the distance between them (in meters). Both of these equations are inverse square laws that describe specific interactions between particles, this explains why they look almost identical and determine the same thing, force.

To find the magnitude of the force alone, simply take the absolute value of the charges, then to make the correct vector formation look at the charges and intuitively determine the direction of the force (if possible). In the case where a particle is being affected by more than one other particle, the net force on it is the sum of the individual forces with the other particles.

Example 01:
The figure shows an arrangement of four charged particles, with an angle q 30 degrees and distance d 2.00 cm. Particle 2 has charge Q2 = 8 x 10^-19 C; particle 3 and 4 have charges Q3 =Q4 = -1.6 x 10^-19C. (a). What is distance D between the origin and particle 2 if the net electrostatic force on particle 1 due to the other particle is zero? (b). If particle 3 and 4 were moved closer to the x axis but maintained their symmetry about that axis, would the required value of D be greater than, less than or the same as in part (a)?


Shell Theorems
An important assumption in these types of situations is that a shell of uniform charge attracts (or repels) a charged particle that is outside the shell as if all the shell’s charge was at the center. In addition, if a charged particle is inside a shell of uniform charge, then there is no net electrostatic force on the particle from the shell, as it is under the same force from the sphere and it all cancels out. This same assumption is made in the situations of gravity, as all of the concentration is assumed to be at the center of the object.

Some materials have more free electrons (also called conduction electrons), defined as the electrons on the outermost shell of the electron configuration; with these electrons they can conduct a charge much better than others. These materials are called conductors and include copper, aluminum, human body, tap water, etc. Insulators however do not carry charge freely, thus they do not have the same effect that a conductor would. Examples of this type of material are dry wood, paper, glass, pure water, etc. Semiconductors are a mix between conductors and insulators, as they can carry an electrical charge, but not as well as conductors (silicon, germanium, etc.). Superconductors however conduct electricity without any resistance, which makes them perfect conductors (LBCO, YBCO, etc.). The current I, measured in amperes (A), is the rate at which charge moves past a point. In other words, it is the rate of change of charge with time. Mathematically, it is determined as:

Elementary Charge
Charges are not actually random numbers, as they are quantized. This means that the charges can only have certain discrete values, or "allowed" values. Any charge (q) can be determined through the equation: q=n*e, where n = ± 1, 2, 3... and e is defined as the elementary charge, which is approximated to be 1.602 x 10^-19 C. This is an important constant as –e is the charge of an electron, and +e is the charge of a proton. Quarks however do not follow this rule, they do not have whole number quantized energies, instead they have charges of e/3 or 2e/3 but they cannot be detected individually.

Static Electricity
Now with all of this information, we can discuss the physics of the following situation: all of us at some point or another, after walking on the carpet with socks or even taking off a sweater, and then touching something get a small electrical shock. Although it may seem complex, the physics behind this is quite simple. During the process of walking, or taking off the sweater, the contact of the fabrics creates a pathway for electrons to move from one to the other. This creates charged objects when originally they were neutral, and this charge gets transported into your body. This is seen in the picture below, where the plastic strip would represent your body, and the piece of cloth would represent the carpet or sweater.

Static electricity in the making
Static Electricity
Now that your body is negatively charged (as you have gained electrons), when you touch a conductor (door knobs, metal in general, etc.) the extra electrons jump from you to the material you have touched, thus making the shock that you feel. Furthermore, because the electrons are simply being redistributed, the sum of all the charges involved remains constant. This leads to the hypothesis of conservation of charge, for which no exceptions have ever been found.

Causes of Static Electricity
  • Contact-induced charge separation
Electrons can be exchanged between materials on contact; materials with weakly bound electrons tend to lose them, while materials with sparsely filled outer shells tend to gain them. This is known as the triboelectric effect and results in one material becoming positively charged and the other negatively charged. The polarity and strength of the charge on a material once they are separated depends on their relative positions in the triboelectric series. The triboelectric effect is the main cause of static electricity as observed in everyday life, and in common high-school science demonstrations involving rubbing different materials together (e.g. fur and an acrylic rod). Contact-induced charge separation causes your hair to stand up and causes static cling (e.g. balloon rubbed on your hair becomes staticly negatively charged, and when it is close enough, it attracts to the positively charged particles in the wall).
Static Discharge from Contact

  • Pressure-induced charge separation
Applied mechanical stress generates a separation of charge in certain types of crystals and ceramics molecules.
  • Heat-induced charge separation
Heating generates a separation of charge in the atoms or molecules of certain materials. All pyroelectric materials are also piezoelectric. The atomic or molecular properties of heat and pressure response are closely related. Hair dryers are a common example for heat-induced charge separation. A hair dryer is essentially a heating element and a fan and as the element heats up, a separation of charge in the atoms of the heating element is created, which can lead to a large static discharge in older hair dryer models. Newer hair dryers are predominantly encased in plastic to try and eleviate the risk of static shock and heat-related injurys.

Old Metal Hair Dryer
New Plastic Hair Dyer

  • Charge-induced charge separation
A charged object brought into the vicinity of an electrically neutral object will cause a separation of charge within the conductor. Charges of the same polarity are repelled and charges of the opposite polarity are attracted. As the force due to the interaction of electric charges falls off rapidly with increasing distance, the effect of the closer (opposite polarity) charges is greater and the two objects feel a force of attraction. The effect is most pronounced when the neutral object is an electrical conductor as the charges are more free to move around.Careful grounding of part of an object with a charge-induced charge separation can permanently add or remove electrons,leaving the object with a global permanent charge. This is why many computer and electronic components are shipped in anti-static packaging. The packaging acts as a type of Faraday cage that surrounds the material inside and keeps charge from entering or leaving the material.
Anti-static Bag

This process is integral to the workings of the Van de Graaff Generator, a device commonly used to demonstrate the effects of static electricity (Video).

Example 1:
Calculate the number of coulombs of positive charge in 250 cm^3 of (neutral) water.


Example 2:
What is the total charge in coulombs of 75.0 kg of electrons?