CBSE · Class 12 · Physics · Chapter 1

Electric Charges and Fields / Electrostatic Potential and Capacitance — Formula Sheet

Board Formulas

16 formulas

1.Coulomb's Law★
$F = \frac{1}{4 π ε _{0}} \frac{q _{1} q _{2}}{r ^{2}} = k \frac{q _{1} q _{2}}{r ^{2}}$
$F$ : Electrostatic force (N) · $k$ : Coulomb's constant = 9×10⁹ N·m²/C² · $ε_{0}$ : Permittivity of free space = 8.85×10⁻¹² C²/(N·m²) · $q_{1}, q_{2}$ : Point charges (C) · $r$ : Distance between charges (m)
Force between two point charges. Attractive if charges opposite, repulsive if same.
2.Electric Field of Point Charge★
$E = \frac{F}{q _{0}} = k \frac{Q}{r ^{2}} r^$
Force per unit positive test charge. Vector — direction is radially away from +Q.
3.Electric Potential of Point Charge
$V = k \frac{Q}{r}$
Work done per unit positive charge to bring it from infinity to point r. Scalar quantity.
4.Relation between E and V
$E = - \frac{d V}{d r}$
Field points from high to low potential. Negative gradient of V.
5.Electric Dipole Moment
$p = q \cdot 2 a$
$p$ : Dipole moment (C·m) · $2 a$ : Distance between the two charges (m)
Magnitude = q × 2a (charge × separation). Direction: from −q to +q.
6.Field on Axial Line of Dipole★
$E_{a x ia l} = \frac{1}{4 π ε _{0}} \frac{2 p}{r ^{3}} (r ≫ a)$
Direction: same as dipole moment p.
7.Field on Equatorial Line of Dipole
$E_{e q} = \frac{1}{4 π ε _{0}} \frac{p}{r ^{3}} (r ≫ a)$
Direction: antiparallel to p. Note: axial field = 2× equatorial field.
8.Gauss's Law★
$\oint E \cdot d A = \frac{q _{e n c}}{ε _{0}}$
Total electric flux through closed surface = enclosed charge / ε₀.
9.Field of Infinite Line Charge
$E = \frac{λ}{2 π ε _{0} r}$
Uses Gauss's law with cylindrical surface. λ = linear charge density (C/m).
10.Field of Infinite Plane Sheet
$E = \frac{σ}{2 ε _{0}}$
Independent of distance from sheet. σ = surface charge density (C/m²).
11.Capacitance
$C = \frac{Q}{V}$
Charge stored per unit potential difference. Unit: farad (F).
12.Parallel-Plate Capacitor★
$C = \frac{ε _{0} A}{d}$
$A$ : Plate area (m²) · $d$ : Separation between plates (m)
Larger area or smaller separation ⇒ higher capacitance.
13.With Dielectric
$C = \frac{K ε _{0} A}{d}$
Dielectric constant K > 1 increases capacitance K-fold.
14.Energy Stored in Capacitor
$U = \frac{1}{2} C V^{2} = \frac{Q ^{2}}{2 C} = \frac{1}{2} Q V$
Three equivalent forms — pick whichever avoids the unknown quantity.
15.Capacitors in Series
$\frac{1}{C _{e q}} = \frac{1}{C _{1}} + \frac{1}{C _{2}} + \dots$
Same charge on each, voltages add. Equivalent capacitance is SMALLER than smallest.
16.Capacitors in Parallel
$C_{e q} = C_{1} + C_{2} + \dots$
Same voltage across each, charges add. Equivalent is LARGER than largest.