Define electric potential at a point. Derive an expression for the potential due to a point charge q at a distance r. Draw the graph of V against r.

1. 1 · Define potential. The work done per unit positive charge to bring it from infinity to the point without acceleration. Unit volt.
2. 2 · Set up. Charge q at O; point P at distance r. Bring a unit positive charge from ∞ to P.
3. 3 · Write the work. W = −∫ q/(4πε₀r′²) dr′, with r′ from ∞ to r.
4. 4 · Integrate. W = q/(4πε₀r). So V = (1/4πε₀) q/r.
5. 5 · Draw the graph. [V on the vertical axis, r on the horizontal axis; a curve falling as 1/r towards the r-axis]
6. 6 · Real life. A bird on one live wire is safe: both its feet are at the same potential.
7. 7 · Close in one line. The potential of a point charge is a scalar that falls as 1/r.

Scoring tip: Write 'from infinity' and 'without acceleration' in the definition. Show the limits ∞ to r on the integral.