Electric Potential: Advanced Guide for JEE Main

Electric potential is the scalar quantity that makes electrostatics calculations manageable: instead of adding field vectors, you add scalar potentials. JEE Main tests it across multiple question types — from potential due to discrete charges to dipole potential, equipotential surfaces, and the E–V relationship — and the marks are consistently available for students who master both the formulas and the geometric intuition.

Potential Due to Point Charges and Systems

The potential due to a point charge q at distance r is V = kq/r (with sign: positive for positive charge, negative for negative charge). For a system of charges, V_total = Σ kqᵢ/rᵢ — scalar addition, no vectors. This is the fundamental advantage over field calculations. Potential energy of two charges: U = kq₁q₂/r. For an equilateral triangle of three charges, the potential at the centroid is simply 3kq/r where r is the distance from each charge to the centroid. For the foundational treatment see our electrostatics complete guide.

Equipotential Surfaces

Equipotential surfaces are the set of all points at the same potential. For a point charge: concentric spheres. For a uniform field: planes perpendicular to the field. Key properties: no work is done moving a charge along an equipotential (W = qΔV = 0); the electric field is always perpendicular to equipotential surfaces; equipotentials never cross. JEE uses these properties in questions about charge paths and in problems asking whether work is done by the electric force during a particular displacement.

The Electric Dipole Potential

For an electric dipole (charges +q and −q separated by 2a, dipole moment p = q × 2a): at a point at distance r (r >> a) making angle θ with the dipole axis: V = kp cosθ/r². On the axial line (θ = 0°): V = kp/r². On the equatorial line (θ = 90°): V = 0. The dipole field: along axis E = 2kp/r³; along equator E = kp/r³. These dipole results appear frequently in both potential and field questions.

The E–V Relationship

The electric field is the negative gradient of potential: E_x = −dV/dx. In a uniform field, E is constant and V varies linearly with distance in the field direction. A common JEE question gives V as a function of position and asks for E — differentiate V with respect to the coordinate. If V = 5x² + 3y: E_x = −10x, E_y = −3, E_z = 0. At position (2, 1, 0): E = (−20 î − 3 ĵ) V/m. Practising this derivative route builds the skill for graph-based questions where V vs. r is plotted.

Potential Energy and Assembled Charge Systems

The potential energy of a system of charges equals the work done to assemble them from infinity. For three charges q₁, q₂, q₃: U = k(q₁q₂/r₁₂ + q₁q₃/r₁₃ + q₂q₃/r₂₃). This is always the sum of all pair interactions. For equilibrium of a charge system, set the net force on each charge to zero. After mastering all the potential concepts and working through applied problems, take a free mock test to consolidate this high-yield chapter.