Lightning

Charge sandbox

drag a charge · cross = center

|E| at the center (cross)—

force on the test charge—

q₁ / q₂ (selected / nearest)—

distance r—

force F (↔ repel, →← attract)—

energy U = kq₁q₂/r—

Setups and view

Selected charge q+2.0 µC Field lines (density ∝ |q|) Equipotential surfaces (constant potential V) Field strength map |E|

F = k q₁q₂r²E = Fq = k qr²k = 1/(4πε₀) ≈ 8.99·10⁹ N·m²/C² · the area is 40 cm wide (30 cm on a phone)

Charles-Augustin de Coulomb measured this law in 1785 with a torsion balance: the twist angle of a thin wire showed how strongly two charged balls repel each other.

Electricity vs. gravity

Two protons at any distance: electric repulsion and gravitational attraction both fall off as 1/r², so their ratio stays constant.

≈ 1.2·10³⁶ ×that's how many times stronger the electric force is than gravity

electric ke²/r² (r = 1 nm)—

gravitational Gm²/r²—

Gravity wins on the scale of planets only because positive and negative charges cancel almost perfectly, while mass always adds up.

Rubbing: who gives electrons to whom?

drag the object over the material

object's charge0 nC

material's charge0 nC

electrons transferred0

charge “leak” time—

Triboelectric series

Object Material

Air humidity30%

↑ readily gives up electrons (+)↓ readily takes them (−)

The order varies a little between sources: it depends on how clean, humid and rough the surfaces are. Charge values in the simulation are approximate.

What a charged object can do

drag the object closer

The electroscope step by step

you can drag the rod too

A zap from the door handle

body voltage U0 kV

charge Q = CU0 µC

energy ½CU²0 mJ

spark (approx. 3 kV/mm)—

Why do you get zapped in winter?

Air humidity30%

In winter the heated air indoors is very dry. A thin film of water settles on damp surfaces, and charge slowly leaks away along it; in dry air it has nowhere to go, so it builds up. Shuffling across a carpet at 10–20% humidity can charge a person up to about 35 kV, at 65–90% only to about 1.5 kV (typical values from electrostatic discharge protection tables).

High voltage, small charge. The body has a capacitance of about 100–200 pF, so even at 10 kV the charge is only about 1.5 µC and the energy a few millijoules. The spark hurts, but it does no harm to a healthy person.
Thresholds (roughly): you feel a discharge from about 3 kV, hear it from about 5 kV, and see a spark from about 10 kV.
Trampoline and sweater. A child's hair stands on end on a trampoline because every bounce rubs against the mat; a wool sweater crackles as you pull it off — that's dozens of tiny sparks.
Car door. The seat rubs against your clothes; when you get out, the charge stays on you. Grab the metal door frame before you step onto the ground — the charge will drain away without a spark.

A conductor in an electric field

cross-section — the field runs from left to right

|E| map

External field E₀10 kV/cm

field inside—

strongest field at the surface—

Points and cages

Charge escapes to the surface. Free electrons in the metal keep moving until their own field exactly cancels the external one. Inside a conductor the field is zero, and all the excess charge sits on the surface.
Points concentrate charge. On a sharply curved surface the charge density and the field are greatest. When the field exceeds about 3 MV/m (30 kV/cm), the air around the point begins to ionize and glow — that's corona discharge, and on ships' masts and aircraft wings it's St. Elmo's fire.
A lightning rod doesn't “ward off” lightning. It gives it a convenient, predictable place to strike and a thick path to the ground that bypasses the walls and the wiring.
Faraday cage. A closed metal mesh shields its interior. When struck by lightning, an airplane or a car with a metal body carries the current along its skin — it's the metal body that protects you, not the tires. The mesh in a microwave oven door stops waves about 12 cm long because its holes are much smaller. A metal elevator can “kill” your phone signal.

Two-dimensional model: a cross-section of long objects, computed numerically on a grid. For a cylinder the field at the surface grows to 2 × E₀; for a sphere in three dimensions it would be 3 × E₀. The electrons' shift is shown in slow motion — in a metal it takes an unimaginably short time.

Parallel-plate capacitor

capacitance C—

charge Q = CU—

voltage U—

field E = U/d—

energy ½CU²—

state—

Build a capacitor

Plate area A100 cm² Gap d1.0 mm Battery voltage100 V

—

C = ε₀ε_r AdQ = CUW = ½CU²ε₀ ≈ 8.85·10⁻¹² F/m · after the battery is disconnected the charge stays, and the voltage changes along with C

A camera flash charges a capacitor for a few seconds and releases the energy (a few joules) in a fraction of a millisecond.
A defibrillator stores about 120–360 J of energy in a capacitor and delivers it in a pulse lasting a few milliseconds.
Supercapacitors reach capacitances of even thousands of farads at about 2.7 V — the huge “surface” is porous carbon.
A touchscreen senses your finger because the finger changes the capacitance of a grid of electrodes under the glass. Computer →

Thundercloud and lightning

drag the cloud · click the ground

Strike by itself at 100% Particles in the cloud

Updraft (charging)medium

Field under the cloud / breakdown threshold0%

strike—

peak current (random, typical)—

strokes in the flash—

hits: lightning rod / other0 / 0

Object heights are greatly exaggerated (the cloud base is usually 1–2 km above the ground), and the stepped leader grows here about 100 times slower than in reality. Successive strokes in one flash are slowed down and dimmed — real ones are tens of milliseconds apart.

≈ 30,000 Kchannel temperature — about 5 times hotter than the surface of the Sun

≈ 30 kAtypical peak current; rarely above 200 kA

tens of µsduration of the current pulse of one return stroke

~1 GJenergy of a flash — mostly heat, light and sound

How far away is the storm?

Thunder sound

0.0 s

Distance to the storm: km

s = v_sound · t ≈ 343 m/s · t3 s ≈ 1 kmlight arrives practically instantly; 343 m/s is the speed of sound in air at 20 °C

Thunder rumbles for a long time because sound from different parts of a channel several kilometers long reaches us from different distances — first from the nearest part, last from the farthest. More about sound waves: String, Doppler effect.

Where to take shelter?

Click one of the eight places (or press its number on the keyboard) to check whether it protects you from lightning.

When thunder roars, go indoors. If you can hear thunder, you are within striking distance of lightning. People used to be taught the 30/30 rule: take shelter when less than 30 s pass between the flash and the thunder, and go back out only 30 minutes after the last thunder — the second part still holds. In Poland, storm warnings are issued by the national weather service IMGW-PIB (three levels), and the government's Alert RCB text-message system warns about dangerous situations. Strikes are tracked in real time by, among others, IMGW-PIB's detection system called PERUN, which picks up the radio waves that lightning gives off.

Van de Graaff generator

dome voltage V0 kV

maximum ≈ E_b·R—

spark across the gap ≈ E_b·g—

dome capacitance 4πε₀R—

Dome and gap

Dome radius R20 cm Ball distance g8 cm

V_max ≈ E_b · RE_b ≈ 3 MV/mthe field at the surface of a sphere is V/R; once it exceeds the dielectric strength of air, the charge leaks away as corona discharge

A rubber belt rubs against a roller and carries charge upward. A brush with sharp points inside the dome collects it, and the charge immediately moves to the outer surface of the metal — which is why you can keep “pouring” it into the dome without end. The voltage rises until the field at the surface reaches the dielectric strength of air.

About 3 kV per millimeter is an approximation for gaps of millimeters to centimeters in dry air. Very short gaps need more, while in long (meter-scale) gaps a spark jumps at a much lower average field. The generator's sparks are spectacular but carry little energy; even so, never go near them with a pacemaker or electronics.

Kelvin water dropper

voltage between the cans0 kV

If the left can is ever so slightly negative, the right ring (connected to it) induces a positive charge in the right-hand drops. They fall into the right can, which through the left ring induces negative drops on the left… Every imbalance feeds itself, so the voltage grows exponentially — from a random difference all the way to more than ten kilovolts. Which sign wins is down to chance every time.

Lichtenberg figures

click to choose the entry point

Branching (exponent η)1.0

The same algorithm builds the lightning bolts in the “Storm” mode: a new piece of channel appears with a probability that grows with the local field strength (the dielectric breakdown model, DBM). In a real acrylic block, charge is injected with an electron beam, and then a tap on a nail triggers a discharge that burns these branching trees into the block.

Electrostatic machines and daring experiments

The two discs spin in opposite directions. The metal sectors of one disc induce charge on the sectors of the other, and brushes collect it into two Leyden jars — until a spark several centimeters long jumps.

The first capacitor: glass between two layers of metal. It was built in 1745 by Ewald von Kleist and a year later in Leiden by Pieter van Musschenbroek, who described a shock so strong that — as he wrote — he would not repeat the experiment “for the crown of France.”

Benjamin Franklin described drawing sparks from a key on the wet string of a kite flown during a thunderstorm and charging a Leyden jar with them. It was extremely dangerous: in 1753, in St. Petersburg, Georg Wilhelm Richmann was killed by lightning during similar measurements. Never try this.

A laser printer in 4 steps

The same idea, xerography, drives photocopiers (Chester Carlson, 1938). See also: Laser →

A precipitator in the smokestack

Electrode voltage50 kV

efficiency (Deutsch model)—

caught in the simulation—

Electrostatic precipitators in power plants and cement plants typically capture over 99% of the dust by mass. Model: η = 1 − e^−wA/Q (drift velocity w, plate area A, flow rate Q); the drift velocity grows roughly with the square of the field. Power plant →

Electrostatic painting

Droplets of paint or powder get a charge at the nozzle, while the object being painted is grounded. The field wraps the paint around the object — it even coats the back of a tube — and much less of it is wasted. That's how car bodies and bicycles are painted.

ESD protection

A spark you won't even feel (below 3 kV) can punch through the nanometer-thin insulating layers in transistors. That's why before handling computer parts you touch grounded metal or wear a wrist strap, and chips are packed in antistatic bags. Computer →

Touchscreen

Under the glass lies a grid of transparent electrodes forming tiny capacitors. Your finger conducts electricity and changes the capacitance where you touch; the controller measures this hundreds of times per second. That's why an ordinary glove doesn't work, but a special one — with conductive threads — does.

Bees and flowers

A bee in flight usually picks up a small positive charge, while a flower on its stem is negatively charged relative to the air. Studies (including one on bumblebees, 2013) suggest that insects sense a flower's field with their hairs and can tell a flower that was just visited. This is still a young field of research.

Ballooning spiders

Young spiders let out silk threads and fly away for hundreds of kilometers. An experiment in 2018 showed that in the lab, with no wind, an electric field alone, of a strength found in the atmosphere, could make them take off and lift them. How big a role this plays outdoors is still being studied.

The global electric circuit

In fair weather over flat ground, the electric field near the surface is about 100 V/m and points downward. The upper atmosphere sits at a potential of about 250 kV relative to the ground, and thunderstorms keep topping up the charge — lightning flashes on Earth about 40–50 times per second on average. Above strong thunderstorms, red sprites and rings called elves appear at altitudes of 50–90 km.

From amber to the lightning rod

c. 600 BCThales of Miletus (according to later accounts) — rubbed amber attracts feathers. The Greek word for amber is ēlektron.
1600William Gilbert, “De Magnete” — distinguishes electricity from magnetism; coins the Latin word electricus. Magnetic field →
1745–1746Leyden jar (von Kleist, van Musschenbroek) — the first capacitor.
1752Benjamin Franklin — lightning is an electric spark; the lightning rod. The kite experiment (and, earlier in France, d'Alibard's tall-rod experiment).
1753Georg Wilhelm Richmann is killed in St. Petersburg while measuring thunderstorm electricity.
1754Prokop Diviš erects a grounded “weather machine” in Přímětice, Moravia — often regarded as the first lightning rod in Europe (though its maker actually meant it to “suck” electricity out of the clouds).
1785Charles-Augustin de Coulomb — the torsion balance and the 1/r² law.
1836Michael Faraday sits in a metal-lined cage with sparks leaping across its outside — the electroscope inside shows nothing.
1897–1909J. J. Thomson discovers the electron, Robert Millikan measures its charge (oil drops): e ≈ 1.602·10⁻¹⁹ C. Particles →

How does it work?

All matter is made of positive nuclei and negative electrons. Usually there are equal amounts of each and the body is neutral. When an object gains or loses electrons, it has an electric charge, measured in coulombs (C). One electron carries −1.602·10⁻¹⁹ C, so 1 µC is an excess of about 6 trillion electrons. Like charges repel, opposite charges attract.

Coulomb's law and the field

F = k |q₁q₂|r²E = FqV = k qr1 µC and 1 µC 10 cm apart repel each other with a force of about 0.9 N — like the weight of 90 g

The electric field tells you what force would act on a small test charge at each point. Field lines start on positive charges, end on negative ones and never cross; where they are dense, the field is strong. The potential V is energy per unit charge, and voltage is a potential difference. Surfaces of constant potential always cross the field lines at right angles.

Conductors, insulators, induction

In a conductor (metal, salty water, the human body) some of the electrons move freely; in an insulator (rubber, glass, plastic) they are bound to their atoms. A body can be charged by friction (electrons move from one material to the other), by contact (the charge spreads over both bodies) and by induction (a nearby charge pushes electrons around in a conductor; grounding lets some of them flow away). In an insulator the charge doesn't flow, but the molecules polarize — which is why a balloon attracts a neutral wall.

Capacitor

C = ε₀ε_r AdQ = CUE = UdW = ½CU²

In a cumulonimbus cloud the updraft carries ice crystals upward while heavier graupel (soft hail pellets) falls. When they collide in the presence of supercooled water, charge passes between them: in a typical storm positive charge gathers at the top of the cloud, the main negative region lies at the height where it is about −10…−20 °C, and near the base there is sometimes a small positive pocket. The details of this mechanism are still being researched. When the field is strong enough to ionize the air, a stepped leader sets off downward — in jumps of several tens of meters, branching as it goes. Upward streamers rise to meet it from tall objects. When they connect, a bright return stroke surges through the channel; more strokes may follow. Within microseconds the air heats up to about 30,000 K, expands violently, and thunder is born.

s ≈ 343 m/s · tV_max ≈ E_b · Rair breaks down at about 3 MV/m (approximation for short gaps)

Simplifications: the sandbox computes the field in 2D from point charges (smoothed right at each charge); the conductor and the cage are a two-dimensional grid model; the amounts of charge from rubbing are approximate; lightning and Lichtenberg figures grow by a simplified breakdown model on a grid, with exaggerated object sizes and slowed-down time.

Lightning

Charge sandbox

Setups and view

Electricity vs. gravity

Rubbing: who gives electrons to whom?

Triboelectric series

What a charged object can do

The electroscope step by step

A zap from the door handle

Why do you get zapped in winter?

A conductor in an electric field

Points and cages

Parallel-plate capacitor

Build a capacitor

Thundercloud and lightning

How far away is the storm?

Where to take shelter?

Van de Graaff generator

Dome and gap

Kelvin water dropper

Lichtenberg figures

Electrostatic machines and daring experiments

A laser printer in 4 steps

A precipitator in the smokestack

Electrostatic painting

ESD protection

Touchscreen

Bees and flowers

Ballooning spiders

The global electric circuit

From amber to the lightning rod

How does it work?

Coulomb's law and the field

Conductors, insulators, induction

Capacitor

Lightning

See also

Challenges

Did you know…?

Keys