Electric potential due to a point charge

For an isolated point charge q kept fixed at the origin, the electric potential at a point P a distance r away is found by computing the work per unit charge required to bring a positive test charge in from infinity to P against the Coulomb field of q, which (after carrying out the integration of the varying force along the path) gives the compact result V = k q/r = q/(4 pi epsilon0 r). Unlike the electric field, the potential due to a point charge is a scalar: it has a definite algebraic sign matching the sign of q (positive charges produce positive potential everywhere around them, negative charges produce negative potential), it has no direction, and it falls off as 1/r rather than 1/r^2, more slowly than the field itself. When several point charges q1, q2, ..., qn are present together, the electric potential they jointly produce at any point P is found by simple algebraic (scalar) superposition rather than vector superposition: V_total(P) = V1(P) + V2(P) + ... + Vn(P) = k[q1/r1 + q2/r2 + ... + qn/rn], where each ri is the distance from charge qi to the point P. Because ordinary numbers, unlike vectors, add without regard to direction, computing the net …