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Electric potential at a point is the work done per unit positive charge in bringing a test charge from infinity to that point: V = W/q_0 = -integral(E.dr). SI unit: volt (V) = J/C. Dimensional formula: [M L^2 T^(-3) A^(-1)]. Potential is a scalar quantity, which is its main computational advantage — potentials from multiple charges add algebraically, not vectorially.

For a point charge Q at distance r: V = kQ/r. Unlike the field (which varies as 1/r^2), potential varies as 1/r. V is positive for positive charges, negative for negative charges, and zero at infinity. The potential difference between two points determines the work done in moving a charge: W = q(V_A - V_B).

Key relationships: E = -dV/dr (field is the negative gradient of potential). E points from high V to low V. Where E = 0, V has a critical point (max, min, or saddle) but need not be zero. Where V = 0, E need not be zero. This distinction is frequently exploited in JEE questions.

For standard configurations: ring on axis V = kQ/sqrt(x^2 + R^2); solid sphere inside V = kQ(3R^2 - r^2)/(2R^3) with V_center = (3/2)V_surface; hollow sphere inside V = kQ/R (constant); dipole V = kp*cos(theta)/r^2. The equatorial plane of a dipole is at V = 0. For infinite line charges and planes, absolute potential diverges — only potential differences are meaningful.