D.2.14 (HL)—Electric potential

Use point-charge potential

Electric potential is signed and has zero at infinity. For source charge $Q$, use distance $r$ from the charge centre. Positive $Q$ gives positive potential; negative $Q$ gives negative potential.

Worked example — negative source

For $Q=-1.00\times10^{-8}\,\mathrm{C}$ at $r=1.00\,\mathrm{m}$, $V_e=(8.99\times10^9)(-1.00\times10^{-8})/(1.00)=-89.9\,\mathrm{V}$. At $2.00\,\mathrm{m}$, it is $-45.0\,\mathrm{V}$: farther away, the negative potential increases toward zero.

Combine sources

For several point charges, calculate each $kQ_i/r_i$ and add the scalar values. Use centre-to-point distance and convert all distances and charges before substitution. The potential does not depend on the test charge used to define it.

Check conducting spheres

Inside a charged conducting sphere in electrostatic equilibrium, the electric field is zero and the potential is constant throughout the interior. The potential need not be zero; it equals the surface potential for the ideal spherical case.

Common trap

Do not use $kQ/r^2$ for potential, and do not assume zero field means zero potential inside a conductor.