# Electric Field and Potential

> Electric field and potential for JEE Physics; point charges, dipoles, relation between E and V, conductors and exam-focused points.

- Canonical URL: https://prepelephant.com/topics/jee/physics/electric-field-and-potential
- Exam / course: JEE · Subject: Physics
- Publisher: PrepElephant (https://prepelephant.com) — Prepared and reviewed by the PrepElephant Academic Review Team
- First published: 2026-10-02
- Last updated: 2026-10-02
- How to cite: "Electric Field and Potential", PrepElephant, https://prepelephant.com/topics/jee/physics/electric-field-and-potential

## Direct answer

The electric field is force per unit positive test charge, E = F/q; the potential is work per unit charge in bringing a test charge from infinity, V = k q/r for a point charge, with k = 1/(4 pi epsilon_0) = 9 × 10^9 in SI units. They are linked by E = −dV/dr: the field points down the steepest fall of potential. Fields add as vectors, potentials as scalars — a distinction JEE exploits constantly.

## What you must remember

- Point charge: E = k q/r^2 outward from positive charges; V = k q/r, negative for negative charges; pair energy U = k q1 q2/r.
- Uniform field between parallel plates: E = V/d; work in moving charge q is W = q (V_final − V_initial), independent of path.
- Dipole (p = charge × separation): axial field 2 k p/r^3, equatorial k p/r^3; potential k p/r^2 on the axis, zero on the equatorial plane.
- Dipole in a uniform field: torque = p E sin(theta), energy U = −p E cos(theta); stable at theta = 0, unstable at 180 degrees; net force zero.
- Conductors: zero field inside and inside cavities (shielding), constant potential throughout, charge on the outer surface.
- Charged spherical shell: E = 0 and V = k q/R (constant) everywhere inside; outside both behave as for a point charge at the centre. Inside a uniformly charged non-conducting sphere, E grows linearly with r.
- Zero field does not imply zero potential, nor the reverse: between equal like charges E vanishes at the midpoint while V does not; on the dipole's equatorial plane V is zero while E is not.

## Common confusion

The persistent error is sign bookkeeping — fields point inward for negative charges, their potentials are negative, and the dipole energy −p E cos(theta) carries its own sign; magnitudes come out right while answers stay wrong. The second classic slip is summing fields and potentials the same way: potential adds algebraically, field only after resolving into components. Remember too that the zero of potential is a reference choice; only differences (and the field, their gradient) are physical.

## Exam-focused takeaway

JEE Main tests field and potential of simple charge arrays, a charge released in a uniform field, work done in moves, and dipole torque as single-correct and numerical-value questions. JEE Advanced prefers equilibrium of an inserted charge, field as the slope of a given V(x) graph, angular dipole problems, Gauss-law crossover for spheres and shells, and the potential energy of three- or four-charge systems. Decide per quantity whether you are adding vectors or scalars, and fix signs at the start.

## Frequently asked questions

### Can E be zero where V is not, and the reverse?

Yes — at the midpoint between equal like charges, E = 0 while V is finite; on a dipole's equatorial plane, V = 0 while E is finite. Field measures how fast potential changes, not its value.

### How are E and V related?

E = −dV/dr: the field component along any direction is minus the potential's rate of change in that direction.

### Why is the field zero inside a conductor?

Free electrons rearrange until their own field cancels the applied one inside — the basis of electrostatic shielding.

### Why is the dipole's aligned state its stable equilibrium?

U = −p E cos(theta) is minimum at theta = 0; the torque p E sin(theta) restores any small rotation, whereas 180 degrees is unstable.

### What are E and V inside a charged shell?

E = 0 everywhere inside, while V stays constant at k q/R — constant, not zero.