Charges on Conductors, Lightning and Lightning Protection – Electric Force and Electric Field (Senior 4 Physics) | Ganzaa

Electric Force and Electric Field

Lessons

Senior 4 · Physics

Electric Force and Electric Field

5 lessons

Lesson 4 of 5

Charges on Conductors, Lightning and Lightning Protection

25 min

The deadliest hazard

In 2025, Rwanda recorded 1270 disaster incidents. Strong winds, floods and landslides damaged homes and fields, but the hazard that took the most lives was lightning: 200 incidents killed 87 people, 61% of all disaster deaths that year, and injured 157 (MINEMA, 2025). The Ministry in charge of Emergency Management recommends lightning protection for schools, health centres and community buildings in the districts most at risk, among them Burera, Gisagara, Rutsiro, Gakenke, Rusizi and Karongi. A lightning flash is electrostatics on the largest scale: charges separated in a cloud, a field strong enough to tear electrons from air molecules, and a sudden discharge. In this lesson you see how charge behaves on conductors, why sharp points matter, how lightning forms, and how buildings and people can be protected.

Charge on conductors

In a conductor, charges move freely. When the charges stop moving (electrostatic equilibrium), four results follow:

the field inside the metal is zero: otherwise free charges would still be moving;
any extra charge sits on the outer surface;
the whole conductor is at one potential, so its surface is an equipotential and field lines leave it at right angles;
the charge is densest where the surface curves most sharply, and the field just outside is strongest there (Figure 4.1).

The last point can be shown with two metal spheres of radii $r_{1}$ and $r_{2}$ joined by a long wire, so they share one potential $V$ . For each sphere $V = \frac{kQ}{r}$ , so $Q \propto r$ , and the field at its surface is

E = \frac{kQ}{r^{2}} = \frac{V}{r}

For the same potential, the smaller sphere has the stronger field. A sharp point is like a sphere of tiny radius, so even a modest voltage gives an enormous field at its tip.

Figure 4.1: Charge on a pear-shaped conductor: thin on the rounded end, crowded at the point, where the field is strongest. The field inside the metal is zero.

Because the field inside a closed conductor is zero, a metal box or cage shields what is inside from outside fields. This is why a car or bus with a metal roof protects its passengers in a thunderstorm: the current of a strike flows round the outside of the metal body.

Definition

Dielectric breakdown of air happens when the electric field is strong enough (about $3 \times 10^{6}\,\mathrm{V\,m^{-1}}$ in dry air at sea level) to pull electrons from air molecules; the ions and electrons then make the air conduct. Point discharge (corona discharge) is the breakdown of air near a sharp, charged point, where the field is concentrated: charge leaks away into the air. Example: a point of radius 0.5 mm reaches $3 \times 10^{6}\,\mathrm{V\,m^{-1}}$ at a potential of only $E r = 3 \times 10^{6} \times 5 \times 10^{-4} = 1.5\,\mathrm{kV}$ .

Worked example 1: two spheres sharing charge

Metal spheres of radius 0.10 m and 0.020 m, far apart, are joined by a thin wire and given a total charge of 12 nC. Find the charge on each, their common potential, and the field at each surface.

Same potential: $\frac{Q_1}{r_1} = \frac{Q_2}{r_2} \Rightarrow \frac{Q_1}{Q_2} = \frac{0.10}{0.020} = 5$ , so $Q_1 = 10\,\mathrm{nC}$ and $Q_2 = 2.0\,\mathrm{nC}$ .

V = \frac{8.99 \times 10^{9} \times 10 \times 10^{-9}}{0.10} = 899\,\mathrm{V}, \qquad E_1 = \frac{V}{r_1} = 9.0 \times 10^{3}\,\mathrm{V\,m^{-1}}, \qquad E_2 = \frac{V}{r_2} = 4.5 \times 10^{4}\,\mathrm{V\,m^{-1}}

The small sphere carries less charge but has five times the surface field. Shrink it to a point and the air beside it breaks down first.

How a thundercloud charges and discharges

Inside a tall thundercloud, strong updrafts carry tiny ice crystals upwards while larger soft hail (graupel) falls or hangs in the middle of the cloud. When they collide, the ice crystals become positively charged and the graupel negatively charged. So the upper part of the cloud becomes positive and the middle and lower part negative, with a small positive pocket near the base (Figure 4.2). The large negative charge repels electrons in the ground below, leaving the ground, and everything on it, positively charged (NWS).

When the field becomes strong enough somewhere, the air breaks down. A faint, branching channel of ionised air, the stepped leader, works its way down from the cloud in jumps of tens of metres. As it nears the ground, the field at tall, pointed objects (trees, masts, rooftops) becomes so strong that upward leaders rise from them. When one meets the stepped leader, the circuit is complete and a huge current, the return stroke, surges up the channel. It heats the air to about 28 000 °C, roughly five times the temperature of the Sun's surface (NWS); the air expands so violently that it makes the shock wave we hear as thunder.

Figure 4.2: The charges in a thundercloud and on the ground below, and a building protected by a lightning conductor.

Worked example 2: why lightning cannot be a simple spark

A cloud base is 1.5 km above the ground. (a) What potential difference would be needed to break down all the air between them at once, if the field were uniform? (b) Measured cloud-to-ground potential differences are typically of order $10^{8}\,\mathrm{V}$ . What does the comparison show?

(a) $V = Ed = 3 \times 10^{6} \times 1500 = 4.5 \times 10^{9}\,\mathrm{V}$ .

(b) The real voltage is about 45 times too small to break down the whole gap. Breakdown therefore cannot happen everywhere at once. It starts where the field is concentrated, at the tips of ice particles and then at the tip of the growing leader, which acts like a sharp point carrying the cloud's potential forward. Each step only has to break down the air just ahead of the tip.

Worked example 3: the energy of a flash, and how far away it was

A flash carries about 10 C of charge through a potential difference of about $1 \times 10^{8}\,\mathrm{V}$ (typical values). (a) Estimate the energy released. (b) The thunder is heard 6.0 s after the flash is seen. How far away was the strike? (Take the speed of sound as $340\,\mathrm{m\,s^{-1}}$ .)

(a) $W \approx QV = 10 \times 1 \times 10^{8} = 1 \times 10^{9}\,\mathrm{J}$ , about 280 kWh: roughly what two or three Rwandans use in electricity in a year (Unit 6, Lesson 1). But it is released in a fraction of a second and scattered as heat, light and sound, so it cannot usefully be collected.

(b) Light arrives almost instantly, so the distance is $340 \times 6.0 = 2.0 \times 10^{3}\,\mathrm{m}$ , about 2 km: close enough to strike again. Every 3 s between flash and thunder is about 1 km.

Protection: lightning conductors, arresters and safe behaviour

Lightning protection systems. A lightning protection system does not stop lightning from striking a building; it gives the strike a safe path. It has three parts (Figure 4.2): air terminals (pointed rods) at the highest points, which launch upward leaders and intercept the strike; thick copper or aluminium down conductors on the outside of the building; and an earth electrode, rods or plates buried in the ground, that spreads the charge into the earth. All parts must be well joined (bonded), so that the current does not jump across gaps and start fires. A complete system also has surge protection devices on incoming power, telephone and data lines, because a strike nearby can send damaging voltage surges along wires (NWS).

Lightning arresters on power lines. A surge (lightning) arrester connects a power line to earth through a material that is an insulator at the normal line voltage but conducts strongly at the very high voltage of a lightning surge, so the surge is diverted to earth instead of destroying transformers.

Safe behaviour. The US National Weather Service advises: "When thunder roars, go indoors." There is no safe place outside in a thunderstorm; the only completely safe places are inside a substantial building with wiring and plumbing, or inside a hard-topped metal vehicle with the windows closed. Tents, open-sided shelters and the shade of a tree are not safe. Wait 30 minutes after the last thunder before going back out. Inside, stay off corded phones, avoid plumbing and keep away from outside windows and doors. A person struck by lightning carries no electric charge and is safe to touch: call for help and start CPR if needed (NWS).

Warning

Safety and common mistakes. (1) Never shelter under a lone tree, in a tent or under an open-sided shelter during a thunderstorm; get into a substantial building or a hard-topped metal vehicle. (2) "Lightning never strikes the same place twice" is false: tall, pointed objects are struck again and again. (3) A lightning rod does not "attract" lightning from far away or "prevent" strikes; it intercepts strikes that would hit the building anyway and leads the current safely to earth. (4) In calculations, the field at the surface of a sphere is $\frac{V}{r}$ only for a sphere; it is not $\frac{V}{d}$ as between plates.

Tip

Points concentrate, cages protect. Sharp points concentrate charge and field, so they break down the air first: that is how leaders grow and how lightning rods work. Closed metal shells keep the field out: that is why a car body or a metal-framed building is a safe place.

Slow-motion video of lightning striking a building (AGU), filmed at 40 000 frames per second in Brazil. Watch the downward leader approach, the many upward leaders rising from the tops of nearby buildings to meet it, and the bright return stroke when one connects, as described in this lesson.

✦

Practice

A hollow metal sphere of radius 5.0 cm carries a charge of $+5.0\,\mathrm{nC}$ . Find the field and the potential just outside its surface, and the field at its centre.
The dome of a Van de Graaff generator has radius 0.20 m. Taking the breakdown field of air as $3.0 \times 10^{6}\,\mathrm{V\,m^{-1}}$ , find the greatest potential it can reach, and the charge on it then.
Two metal spheres of radius 0.30 m and 0.10 m, far apart, are joined by a wire and share a total charge of 8.0 nC. Find the charge on each, their potential and the field at each surface.
You see a flash of lightning and hear the thunder 12 s later. How far away was the strike? Should you go indoors? Explain.
A lightning stroke transfers 15 C in 0.50 ms. Find the average current.
Explain, using the idea of the field inside a conductor, why a person inside a car with a metal roof is safe if lightning strikes the car.
Explain why the air terminal of a lightning conductor is pointed, and why the down conductor must be thick and connected to a buried earth electrode.
MINEMA recommends lightning protection for schools in high-risk districts. Evaluate this recommendation: what would it protect, what would it not protect, and what else is needed to reduce deaths?

Show answersHide answers

$E = \frac{8.99 \times 10^{9} \times 5.0 \times 10^{-9}}{0.050^{2}} = 1.8 \times 10^{4}\,\mathrm{V\,m^{-1}}$ ; $V = \frac{8.99 \times 10^{9} \times 5.0 \times 10^{-9}}{0.050} = 899\,\mathrm{V}$ ; at the centre $E = 0$ .
$V_{\max} = E r = 3.0 \times 10^{6} \times 0.20 = 6.0 \times 10^{5}\,\mathrm{V}$ ; $Q = \frac{Vr}{k} = \frac{6.0 \times 10^{5} \times 0.20}{8.99 \times 10^{9}} = 1.3 \times 10^{-5}\,\mathrm{C}$ (13 μC).
$Q \propto r$ : 6.0 nC and 2.0 nC; $V = \frac{8.99 \times 10^{9} \times 6.0 \times 10^{-9}}{0.30} = 180\,\mathrm{V}$ ; $E_1 = \frac{180}{0.30} = 600\,\mathrm{V\,m^{-1}}$ , $E_2 = \frac{180}{0.10} = 1.8 \times 10^{3}\,\mathrm{V\,m^{-1}}$ .
$340 \times 12 = 4.1 \times 10^{3}\,\mathrm{m}$ , about 4 km. Yes: if you can hear thunder you are within striking distance of the storm. Go indoors and wait 30 minutes after the last thunder.
$I = \frac{Q}{t} = \frac{15}{5.0 \times 10^{-4}} = 3.0 \times 10^{4}\,\mathrm{A}$ .
The metal body is a closed conductor. The charge and current of the strike stay on and flow over its outer surface to the ground (often jumping the tyres), and the field inside the metal shell is close to zero, so no current passes through the people inside (as long as they do not touch metal parts connected to the outside).
A point has a tiny radius of curvature, so the field at its tip is very strong and it launches an upward leader that meets the downward leader. The down conductor must carry a current of tens of thousands of amperes without melting, so it must have a low resistance (thick metal), and it must end in a good earth so that the charge spreads into the ground instead of jumping into the building.
Protection would make the protected buildings safe places for the pupils and staff inside, and stop fires and damage to electrical equipment (with surge protection). It would not protect people outdoors, on the way to school, in fields or on the water, where many victims are struck. Deaths are also reduced by teaching people the warning signs and safe sheltering ("when thunder roars, go indoors"), by weather warnings, and by first aid: a person struck by lightning carries no charge and can be safely touched and given CPR.

Quick check

A pear-shaped metal conductor is charged. Where is the field just outside its surface strongest?

Key points

In a conductor at equilibrium: $E = 0$ inside, charge on the outer surface, the surface is an equipotential, and the charge and field are greatest at sharp points ( $E = \frac{V}{r}$ for a sphere).
Air breaks down at about $3 \times 10^{6}\,\mathrm{V\,m^{-1}}$ ; sharp points cause point discharge.
Thunderclouds separate charge by ice–graupel collisions; stepped leaders and upward leaders meet, and the return stroke follows. In 2025 lightning caused 61% of Rwanda's disaster deaths (MINEMA).
Protection: air terminal, down conductor, earth electrode and surge protection; arresters guard power lines. When thunder roars, go indoors; wait 30 minutes after the last thunder.

Sources and credits

Rwandan facts: Ministry in charge of Emergency Management (MINEMA), Rwanda Disaster Effects Situation Report 2025 (December 2025).
Lightning science and safety: US National Weather Service, Understanding Lightning: Thunderstorm Electrification, Lightning Science overview, Lightning Safety overview, When a Safe Building or Vehicle is Nearby, Lightning Indoors and Lightning Rods, read October 2026.
Photo: Lightning NOAA by C. Clark, NOAA Photo Library, Wikimedia Commons, public domain.
Photo: Lightning rod, Woodland Plantation House, LaPlace, Louisiana by Infrogmation of New Orleans, Wikimedia Commons, licensed under CC BY-SA 4.0.
Video: Slow-motion video of lightning striking a building, AGU, embedded from YouTube.

Written by Ganzaa: the lesson text, derivations, diagrams, worked examples and practice exercises. This lesson adapts CC BY-SA material and is shared under CC BY-SA 4.0.

1The deadliest hazard

2Charge on conductors

3How a thundercloud charges and discharges

4Protection: lightning conductors, arresters and safe behaviour

The deadliest hazard

Charge on conductors

How a thundercloud charges and discharges

Protection: lightning conductors, arresters and safe behaviour