Maharashtra State Board · Class 12 · Physics · Chapter 8

Electrostatics — Formula Sheet

Board Formulas

13 formulas

1.Coulomb's Law (vector form)★
$F_{12} = \frac{1}{4 π ε _{0}} \frac{q _{1} q _{2}}{r ^{2}} r^_{12}$
$F_{12}$ : Force on q₁ due to q₂ (N) · $ε_{0}$ : Permittivity of free space = 8.854×10⁻¹² C²·N⁻¹·m⁻² · $q_{1}, q_{2}$ : Interacting point charges (C) · $r$ : Separation between charges (m)
Force on charge 1 due to charge 2. r̂₁₂ points from 2 to 1. Same sign ⇒ repulsion, opposite sign ⇒ attraction.
2.Electric Field Intensity★
$E = lim_{q_{0} \to 0} \frac{F}{q _{0}} = \frac{1}{4 π ε _{0}} \frac{q}{r ^{2}} r^$
Force per unit positive test charge in the limit q₀ → 0. Vector, radially outward from +q.
3.Electric Dipole Moment
$p = q \cdot 2 l$
$2 l$ : Length of the dipole (m) · $q$ : Magnitude of either charge (C)
Vector directed from −q to +q. Magnitude p = q(2l). SI unit: C·m.
4.Field on Axial Line of a Short Dipole★
$E_{a} = \frac{1}{4 π ε _{0}} \frac{2 p}{r ^{3}} (r ≫ l)$
Direction: parallel to p. HSC Board derivation question — start by writing E₊ and E₋ separately.
5.Field on Equatorial Line of a Short Dipole★
$E_{e q} = \frac{1}{4 π ε _{0}} \frac{p}{r ^{3}} (r ≫ l)$
Direction: antiparallel to p. Axial field is twice the equatorial field.
6.Torque on a Dipole in Uniform Field
$τ = p \times E, τ = pE sin θ$
Zero at θ = 0 (stable) and θ = π (unstable). Maximum at θ = 90°.
7.Gauss's Theorem★
$\oint_{S} E \cdot d S = \frac{Q _{e n c}}{ε _{0}}$
Total electric flux through any closed (Gaussian) surface = (net charge enclosed)/ε₀.
8.Field due to an Infinite Line of Charge
$E = \frac{λ}{2 π ε _{0} r}$
Cylindrical Gaussian surface, λ = linear charge density (C/m).
9.Field due to an Infinite Plane Sheet
$E = \frac{σ}{2 ε _{0}}$
Independent of distance from the sheet. σ = surface charge density.
10.Capacitance of a Parallel-Plate Capacitor★
$C = \frac{ε _{0} A}{d}$
$A$ : Common plate area (m²) · $d$ : Plate separation (m)
Depends only on plate area, separation, and medium. Not on Q or V.
11.Capacitor with Dielectric Slab★
$C = \frac{ε _{0} A}{d - t ( 1 - \frac{1}{K} )}$
t = thickness of slab, K = dielectric constant. Reduces to Kε₀A/d when t = d.
12.Energy Stored in a Capacitor
$U = \frac{1}{2} C V^{2} = \frac{Q ^{2}}{2 C} = \frac{1}{2} Q V$
All three forms are equivalent — pick the form that avoids the unknown quantity.
13.Energy Density of Electric Field
$u = \frac{1}{2} ε_{0} E^{2}$
Energy per unit volume between capacitor plates. HOTS 2-marker.