Electrostatics: Charging, the Electroscope and Lightning

Charges at Rest

Comb your hair on a dry day and the comb picks up bits of paper. Pull off a polyester shirt in the dark and you may see tiny sparks. During the harmattan, a car door can give you a sharp shock. These are all effects of electrostatics, the study of electric charges at rest. This tutorial covers electrostatics as tested in WAEC, NECO and JAMB physics: the nature of charge, conductors and insulators, charging by friction, contact and induction, the gold-leaf electroscope, how charge is distributed on a conductor, action at points and the lightning conductor, and everyday uses and hazards of static electricity. The tutorial on electric fields and Coulomb's law takes the calculations further.

The Nature of Electric Charge

All matter is made of atoms. Each atom has a positively charged nucleus (containing protons) surrounded by negatively charged electrons. A neutral atom has equal numbers of protons and electrons.

There are two kinds of charge: positive and negative.
Like charges repel; unlike charges attract. This is the fundamental law of electrostatics.
Objects become charged by gaining or losing electrons. Protons are locked in the nucleus and do not move. A body with extra electrons is negatively charged; a body that has lost electrons is positively charged.
Charge is measured in coulombs (C). The charge on one electron is e = −1.6 × 10⁻¹⁹ C, and every charge is a whole-number multiple of e: q = ne. We say charge is quantised.
Charge is conserved: it cannot be created or destroyed, only transferred.

Worked example 1

A plastic rod acquires a charge of −4.8 × 10⁻⁹ C after rubbing. How many extra electrons does it carry?

n = q ÷ e = 4.8 × 10⁻⁹ ÷ 1.6 × 10⁻¹⁹ = 3 × 10¹⁰ electrons.

Conductors and Insulators

In conductors, such as metals, graphite, the human body and the earth, some electrons are free to move through the material, so charge spreads over the whole object. In insulators, such as plastic, glass, rubber, silk, dry wood and dry air, the electrons are tightly bound, so charge stays where it is placed.

This is why insulators are easy to charge by rubbing, while a metal rod held in the hand cannot be charged this way: any charge flows away through the body to the earth. A metal rod can be charged by friction only if it has an insulating handle.

Methods of Charging

1. Charging by friction

When two different insulators are rubbed together, electrons are transferred from one to the other. The two bodies end up with equal and opposite charges.

A glass rod rubbed with silk loses electrons and becomes positive. The silk becomes negative.
An ebonite or polythene rod rubbed with fur or wool gains electrons and becomes negative. The fur becomes positive.

2. Charging by contact (conduction)

When a charged body touches a neutral conductor, some charge flows onto it. The conductor gains charge of the same sign as the charging body.

When two identical conducting spheres touch, the total charge is shared equally between them. For example, if a sphere carrying +8 μC touches an identical sphere carrying −2 μC, the total is +6 μC, so each ends with +3 μC.

3. Charging by induction

Induction charges a conductor without touching it, and the charge produced is opposite in sign to the inducing charge. To charge a metal sphere on an insulating stand positively:

Bring a negatively charged rod near the sphere, without touching. Free electrons in the sphere are repelled to the far side, leaving the near side positive.
With the rod still in place, earth the sphere by touching it with a finger. The repelled electrons flow away to the earth.
Remove the finger (the earth connection) first, while the rod is still near.
Then remove the rod. The sphere is left with a net positive charge, which spreads over its surface.

The order of steps 3 and 4 matters. If the rod is removed first, the electrons flow back from the earth and the sphere ends up neutral.

Induction also explains why a charged comb attracts neutral bits of paper: the comb induces an opposite charge on the near side of the paper, and the attraction to the nearer charge is stronger than the repulsion from the farther charge.

The Gold-Leaf Electroscope

The gold-leaf electroscope is a simple instrument for detecting and testing charge. A brass rod passes through an insulating plug into a glass-fronted metal case. A brass cap sits on top of the rod, and a thin gold leaf is attached beside a brass plate at the bottom. When the electroscope is charged, the leaf and plate carry like charges, so the leaf diverges (rises away from the plate).

Uses of the electroscope

Detecting charge: bring a body near the cap. If the leaf diverges, the body is charged.
Finding the sign of a charge: first charge the electroscope with a known charge, say positive. Bring the test body near the cap. If the divergence increases, the body has the same charge (positive). If the divergence decreases, the body is either oppositely charged or uncharged.
Distinguishing conductors from insulators: touch the cap of a charged electroscope with the material, held in the hand. If the leaf collapses quickly, the material is a good conductor. If it collapses slowly, it is a poor conductor. If there is no change, it is an insulator.
Comparing amounts of charge: a larger divergence indicates a larger charge (or potential).

Note: an increase in divergence is the only sure test of the sign of a charge. A decrease could be caused by an uncharged conductor, which becomes charged by induction.

Distribution of Charge on a Conductor

On a charged conductor, the charge resides entirely on the outer surface. There is no charge inside a hollow conductor, which can be shown with Faraday's ice-pail experiment and a proof plane.
The charge is not spread evenly on an irregular conductor. The surface density of charge (charge per unit area) is greatest at sharp points and edges, and smallest on flat or gently curved parts.
On a sphere, the charge is spread uniformly, because every part of the surface has the same curvature.

Action at Points and the Lightning Conductor

Because charge concentrates at sharp points, the electric field there can become strong enough to ionise the surrounding air. Ions with the same charge as the point are repelled, forming an "electric wind", while opposite ions are attracted to the point and neutralise its charge. This is called action at points (or corona discharge), and it allows a pointed conductor to leak its charge away.

A lightning conductor uses this effect. It is a thick copper strip running from sharp spikes above the highest point of a building down to a metal plate buried in damp earth.

When a charged thundercloud passes overhead, it induces an opposite charge on the spikes. Action at points sprays ions upwards, which partly neutralises the charge in the cloud and reduces the chance of a strike.
If lightning does strike, the thick copper strip provides a low-resistance path that carries the huge current safely to the earth, instead of through the building.

During a thunderstorm, avoid standing under isolated tall trees or in open fields, and stay off rooftops. A car with a metal body is relatively safe, because charge stays on the outside of a conductor.

Uses and Hazards of Electrostatics

Uses

Photocopiers and laser printers use a charged drum to attract toner powder to the image.
Electrostatic spray painting charges the paint droplets so they are attracted to the oppositely charged car body, giving an even coat with little waste.
Electrostatic precipitators in factory chimneys charge smoke particles and collect them on plates, reducing air pollution.
The Van de Graaff generator builds up very high voltages for research and demonstrations.

Hazards

Fuel flowing through pipes can become charged by friction, and a spark could ignite the vapour. Petrol tankers and aircraft are earthed before refuelling.
Static sparks can damage sensitive electronic components, so technicians wear earthing wrist straps.
Dust explosions can be triggered by static sparks in flour mills and mines.

Electrostatics: Practice Questions

A body loses 5 × 10¹² electrons. What is its charge?
Two identical metal spheres carry +10 μC and −4 μC. They are brought into contact and then separated. What is the charge on each?
Why can a brass rod held in the bare hand not be charged by rubbing?
A positively charged electroscope is approached by a rod, and the leaf divergence increases. What is the charge on the rod?
State two functions of a lightning conductor.

Answers: 1. q = 5 × 10¹² × 1.6 × 10⁻¹⁹ = +8 × 10⁻⁷ C (positive, since electrons were lost). 2. Total +6 μC, so +3 μC each. 3. Brass is a conductor, so the charge flows through the hand and body to the earth. 4. Positive. 5. It discharges the cloud by action at points, and it conducts a lightning strike safely to the earth.

Conclusion

Electrostatics rests on a few ideas: like charges repel and unlike charges attract, bodies become charged by gaining or losing electrons, and charge is conserved and quantised. Insulators are charged by friction, conductors by contact or induction, and induction always gives the opposite charge. The gold-leaf electroscope detects and tests charge, with an increase in divergence as the sure test of sign. Charge sits on the outside of a conductor and crowds at sharp points, which is the principle behind the lightning conductor.