Electric Potential — Near a Nanocoulomb (Worked Example)

Given

• Q = 1.0 nC = 1.0 × 10⁻⁹ C

• r = 5.0 cm = 0.050 m

Find

The potential V.

Principle

V = kQ/r gives the potential at any distance from a point charge.

Formula

Solution

1. Convert: $r = 0.050\ \mathrm{m}$

2. Substitute: $V = (8.99 \times 10^9)(1.0 \times 10^{-9})/0.050$

3. Numerator: $8.99$

4. Divide: $V = 180\ \mathrm{V}$

Unit check

N·m²/C² × C ÷ m = V — correct.

What this means physically

180 V — a small static charge creates mains-level voltage nearby. Voltage alone is not dangerous; it is the available charge (current) that matters.