9 min readPathway sheetSection B long answer (5 marks), often with a choice: principle, labelled diagram and working; Section A objective parts on corona discharge

Van de Graaff generator

Sharp combs spray charge onto a moving belt, which carries it inside a hollow metal dome. The charge moves to the outer surface, building millions of volts.

Principle 1Charge given to the inside of a hollow conductor moves at once to its outer surface

Principle 2At sharp points the field is so strong that it ionises the air (corona discharge), so charge can be sprayed on or off

Voltage reachedA few million volts: about 5 MV is usual, and some machines reach about 20 MV

UseAccelerating charged particles (ions) to high energies to study nuclear reactions

What it is and why it works

A Van de Graaff generator is an electrostatic machine that builds up a few million volts. It is named after its designer, Robert J. van de Graaff. It rests on two ideas. First, charge given to the inside of a hollow conductor moves at once to its outer surface. So the inside stays free, and more charge can always be added from inside. Second, at sharp points the charge density and the field are very high. The field ionises the air near the points: this is corona discharge. So a comb of sharp needles can spray charge onto a body, or collect charge from it.

Parts of the machine

S: a large hollow metal sphere (dome) on an insulating stand.
Belt: a long belt of insulating material, such as rubber or silk, running over two pulleys.
P₁ and P₂: pulley P₁ near the bottom, turned by an electric motor M; pulley P₂ at the centre of the sphere.
C₁ (spray comb): a comb of sharp metal needles near P₁, kept at about 10⁴ V positive by a power supply.
C₂ (collecting comb): a comb of needles near P₂, joined to the inner surface of the sphere.
T: an earthed metal chamber round the whole machine, filled with air at high pressure.

How charge reaches the dome

Working, step by step

1
The motor turns pulley P₁, so the belt runs continuously.
2
The field near the needles of C₁ is very strong. It ionises the air: this is corona discharge.
3
Negative ions move to C₁ and are neutralised; the supply keeps C₁ positive. Positive ions are pushed onto the belt.
4
The belt carries this positive charge up inside the sphere S.
5
At C₂ there is corona discharge again. Negative ions from the air neutralise the belt, and positive charge passes through C₂ to the sphere.
6
The sphere at once moves this charge to its outer surface, so its inside stays free to take more.
7★
So, charge keeps piling up on S, and its potential rises to a few million volts. Leakage into the air sets the limit; the earthed chamber T, filled with air at high pressure, cuts this leakage down.

★ key step

How to draw the Van de Graaff generator

1
Draw a large circle at the top for the sphere S, on a tall column labelled insulating stand.
2
Draw pulley P₂ inside the sphere and pulley P₁ at the bottom. Join them with a long belt: two vertical lines.
3
Draw a motor M joined to P₁.
4
Draw comb C₁ as a row of short spikes pointing at the belt near P₁. Join it to a power supply, and join the other side of the supply to earth.
5
Draw comb C₂ as spikes pointing at the belt near P₂, joined to the inside of the sphere.
6
Put + signs on the rising side of the belt and on the outside of S. Draw a dashed outline round everything and label it earthed chamber T.

Worked example: how much charge can the dome hold?

Problem

Air breaks down when the field reaches about 3 × 10⁶ N C⁻¹. The dome of a Van de Graaff generator is a sphere of radius 0.50 m. Find the largest charge it can hold in open air. (1/4πε₀ = 9 × 10⁹ N m² C⁻²)

Working

Outside a charged sphere, E = kQ/r², as if all the charge were at the centre (Gauss's theorem).
The field is strongest at the surface, r = 0.50 m. Set it equal to the breakdown value.
Q = Er²/k = 3 × 10⁶ × (0.50)² ÷ (9 × 10⁹).
Q = 7.5 × 10⁵ ÷ (9 × 10⁹) ≈ 8.3 × 10⁻⁵ C.
A bigger dome, or air at high pressure round it, lets it hold more charge before it sparks.

Answer

About 8.3 × 10⁻⁵ C (83 μC)

In real life

Large Van de Graaff machines are used as particle accelerators in nuclear physics laboratories. Small ones in science centres make a visitor's hair stand on end, because like charges on the hairs repel.

Exam angle

1 marks: “What is corona discharge?” The ionisation of air near a sharp, highly charged point, caused by the very strong field there.

2 marks: “Why does the charge collected by comb C₂ move to the outer surface of the sphere?” Charge given to the inside of a hollow conductor always moves to its outer surface. So the inside stays free of charge and can keep accepting more from the belt.

5 marks: “Explain the principle, construction and working of a Van de Graaff generator with a labelled diagram. Give one use.” Principle: charge on a hollow conductor goes to its outer surface; corona discharge at sharp points. Parts: dome S, insulating belt, pulleys, motor, combs C₁ and C₂, earthed chamber T. Working: corona at C₁ charges the belt; the belt carries charge in; C₂ passes it to S; S reaches millions of volts. Use: accelerating ions for nuclear reactions.

Remember it

Spray, carry, collect, store: comb C₁ sprays, the belt carries, comb C₂ collects, and the dome stores the charge on its outside.