Electrostatics formulas for JEE Main & Advanced

23 formula entries for Electrostatics, in the order the chapter builds them. Each shows the formula, when to use it and the first trap to avoid.

Coulomb's Law

F = \frac{1}{4 π ϵ_{0}} \frac{q_{1} q_{2}}{r^{2}}

When to use. Use to calculate the magnitude of electrostatic force between two point charges in vacuum or a medium.

Trap. Forgetting that the force is along the line joining the charges and can be attractive or repulsive.

Electric Field

\vec{E} = \frac{\vec{F}}{q_{0}}

When to use. Use to find the electric field due to a point charge or a system of charges.

Trap. Thinking the field direction is the same as the force on a negative charge; it's opposite.

Electric Field Due to a Point Charge

\vec{E} = \frac{1}{4 π ϵ_{0}} \frac{q}{r^{2}} \hat{r}

When to use. Use to compute electric field magnitude and direction from a single point charge.

Trap. Forgetting the direction: positive charge gives outward field, negative gives inward.

Electric Dipole

\vec{p} = q \vec{d}

When to use. Use to characterize a dipole in electric fields, especially for torque and potential energy.

Trap. Thinking dipole moment direction is from positive to negative; it's from negative to positive.

Electric Field Due to a Dipole

E_{axial} = \frac{1}{4 π ϵ_{0}} \frac{2 p}{r^{3}}

E_{equatorial} = \frac{1}{4 π ϵ_{0}} \frac{p}{r^{3}}

When to use. Use to find electric field at large distances from a dipole along its axis or perpendicular to it.

Trap. Forgetting that these are approximations for $r ≫ d$ .

Electric Flux

Φ_{E} = \vec{E} \cdot \vec{A} = E A \cos θ

When to use. Use to calculate flux through a surface in uniform fields, or as a step in Gauss's law.

Trap. Forgetting that area vector is perpendicular to the surface.

Gauss's Law

\oint \vec{E} \cdot d \vec{A} = \frac{Q_{enc}}{ϵ_{0}}

When to use. Use to find electric field for symmetric charge distributions (spherical, cylindrical, planar).

Trap. Forgetting that the surface must be closed (Gaussian surface).

Applying Gauss's Law for Spherical Symmetry

\oint \vec{E} \cdot d \vec{A} = E \cdot 4 π r^{2} = \frac{Q_{enc}}{ϵ_{0}}

When to use. Use for uniformly charged spheres, spherical shells, or point charges.

Trap. Forgetting to consider the enclosed charge correctly for points inside the sphere (only charge inside radius r).

Applying Gauss's Law for Cylindrical Symmetry

\oint \vec{E} \cdot d \vec{A} = E \cdot 2 π r L = \frac{Q_{enc}}{ϵ_{0}}

When to use. Use for infinite line charges, infinite cylindrical shells, or infinite cylinders with uniform charge density.

Trap. Forgetting that the ends of the cylinder contribute zero flux because field is parallel to them.

Applying Gauss's Law for Planar Symmetry

\oint \vec{E} \cdot d \vec{A} = 2 E A = \frac{σ A}{ϵ_{0}}

E = \frac{σ}{2 ϵ_{0}}

When to use. Use for infinite plane sheets of charge, or for parallel plate capacitors.

Trap. Forgetting that the field is independent of distance from the plane.

Electric Potential

V = \frac{W}{q_{0}} = - \int_{\infty}^{r} \vec{E} \cdot d \vec{r}

When to use. Use to find potential due to point charges or continuous distributions, and to find work done.

Trap. Thinking potential is a vector; it's a scalar.

Potential Due to a Point Charge

V = \frac{1}{4 π ϵ_{0}} \frac{q}{r}

When to use. Use to find potential at a point due to a single point charge.

Trap. Forgetting that potential is a scalar, so signs of charges matter.

Potential Due to a Dipole

V = \frac{1}{4 π ϵ_{0}} \frac{p \cos θ}{r^{2}}

When to use. Use to find potential at large distances from a dipole.

Trap. Forgetting that this is valid only for $r ≫ d$ .

Equipotential Surface

Δ V = 0

on the surface

When to use. Use to visualize electric fields and to find work done in moving charges.

Trap. Thinking electric field is zero on an equipotential surface; it's perpendicular to it.

Relation Between Electric Field and Potential

\vec{E} = - \nabla V = - (\frac{\partial V}{\partial x} \hat{i} + \frac{\partial V}{\partial y} \hat{j} + \frac{\partial V}{\partial z} \hat{k})

When to use. Use to find electric field from a given potential function, or to find potential from field by integration.

Trap. Forgetting the negative sign: field points from high to low potential.

Conductor in Electrostatic Equilibrium

{\vec{E}}_{inside} = 0

V_{inside} = constant

When to use. Use to analyze conductors in electric fields, such as in capacitors or shielding.

Trap. Thinking there is field inside a conductor even when charges are moving; equilibrium means no current.

Method of Images for Conductors

q_{image} = - q

at mirror location

When to use. Use to find electric field and potential for a point charge near a grounded conducting plane.

Trap. Forgetting that the method only works for grounded conductors (potential zero).

Capacitance

C = \frac{Q}{V}

When to use. Use to characterize capacitors in circuits.

Trap. Thinking capacitance depends on charge; it depends on geometry and dielectric.

Capacitance of a Parallel Plate Capacitor

C = \frac{ϵ_{0} A}{d}

(vacuum),

C = \frac{ϵ_{0} ϵ_{r} A}{d}

(with dielectric)

When to use. Use to find capacitance of a parallel plate capacitor.

Trap. Forgetting that the formula assumes plates are large compared to separation (fringing ignored).

Energy Stored in a Capacitor

U = \frac{1}{2} C V^{2} = \frac{1}{2} Q V = \frac{Q^{2}}{2 C}

When to use. Use to find energy stored in a capacitor or to find work done in charging.

Trap. Forgetting that the energy is stored in the electric field between the plates.

Combination of Capacitors: Series and Parallel

\frac{1}{C_{eq}} = \sum \frac{1}{C_{i}}

(series),

C_{eq} = \sum C_{i}

(parallel)

When to use. Use to find equivalent capacitance in circuits with multiple capacitors.

Trap. Forgetting that in series, charge on each capacitor is the same, but voltage divides.

Dielectric and Polarization

\vec{P} = ϵ_{0} χ_{e} \vec{E}

ϵ_{r} = 1 + χ_{e}

When to use. Use to understand the effect of dielectrics on capacitance and electric fields.

Trap. Thinking dielectrics conduct electricity; they are insulators.

Gauss's Law in Dielectrics

\oint \vec{D} \cdot d \vec{A} = Q_{free, enc}

, where

\vec{D} = ϵ_{0} ϵ_{r} \vec{E}

When to use. Use to find electric field in dielectrics when free charge distribution is known.

Trap. Forgetting that D is due to free charges only, while E is due to all charges (free and bound).

Values to remember

$\frac{1}{4 π ϵ_{0}} = 9 \times 10^{9} {N m}^{2} / C^{2}$ Coulomb's Law
$ϵ_{0} = 8.85 \times 10^{- 12} C^{2} / {N m}^{2}$ Coulomb's Law
$\vec{E} = \frac{1}{4 π ϵ_{0}} \frac{q}{r^{2}} \hat{r}$ Electric Field
$ϵ_{0} = 8.85 \times 10^{- 12} F/m$ Capacitance of a Parallel Plate Capacitor

Read the full chapter: Electrostatics for JEE, with what JEE asks and the common traps.