Electric Potential

Electric Potential

Electric potential V is the potential energy per unit charge at a point in space. For a point charge:

V = rac{kq}{r}

• V — electric potential (volts, J/C)
• k = $8.99 imes 10^9 ext{ N·m}^2/ ext{C}^2$
• q — source charge (C)
• r — distance from charge (m)

Field vs Potential

The field is the (negative) gradient of the potential: $E = -dV/dr$.

Potential Energy of Two Charges

The energy stored in a pair of charges is:

U = rac{k q_1 q_2}{r}

Positive for like charges (repulsive — you must do work to push them together), negative for opposite charges (attractive — they release energy as they approach).

Examples (q = 1 μC)

Your Task

Implement electric_potential(q, r) returning V in volts.