Electric Potential — Van de Graaff Generator (Worked Example)

Given

• Q = 5.0 μC = 5.0 × 10⁻⁶ C

• r = 0.20 m

• k = 8.99 × 10⁹ N·m²/C²

Find

The potential V.

Principle

Outside a charged sphere, the potential is V = kQ/r — as if all charge sat at the centre.

Formula

Solution

1. Write the formula: $V = kQ/r$

2. Substitute: $V = (8.99 \times 10^9)(5.0 \times 10^{-6})/0.20$

3. Numerator: $4.495 \times 10^4$

4. Divide: $V = 2.25 \times 10^5\ \mathrm{V}$

Unit check

N·m²/C² × C ÷ m = N·m/C = J/C = V — correct.

What this means physically

225,000 V — enough to throw dramatic sparks several centimetres long. Museum generators reach millions of volts with bigger domes and more charge.