Maharashtra State Board · Class 12 · Physics · Chapter 12

Electromagnetic Induction — Formula Sheet

Board Formulas

12 formulas

1.Magnetic Flux
$Φ_{B} = B \cdot A = B A cos θ$
θ is angle between B and the area vector A. SI unit: weber (Wb) = T·m².
2.Faraday's Law of Induction★
$ε = - \frac{d Φ _{B}}{d t}$
Induced EMF equals negative rate of change of flux. Negative sign expresses Lenz's law.
3.Motional EMF★
$ε = B v l$
Rod of length l moving with velocity v perpendicular to a magnetic field B.
4.Self-Inductance
$ε = - L \frac{d I}{d t} Φ = L I$
$L$ : Self-inductance (H)
L depends on geometry and material. SI unit: henry (H).
5.Self-Inductance of a Solenoid★
$L = μ_{0} n^{2} A l$
n = turns per unit length, A = cross-sectional area, l = length. Independent of current.
6.Mutual Inductance
$ε_{2} = - M \frac{d I _{1}}{d t}$
M is symmetric: M₁₂ = M₂₁. Basis of transformer action.
7.Mutual Inductance of Coaxial Solenoids★
$M = μ_{0} n_{1} n_{2} A l$
Inner solenoid area A, common length l, turn densities n₁ and n₂.
8.Energy Stored in an Inductor
$U_{L} = \frac{1}{2} L I^{2}$
Analogous to (1/2)CV² for capacitor. Energy density = B²/(2μ₀).
9.AC Generator EMF★
$ε = ε_{0} sin (ω t), ε_{0} = N B A ω$
N = number of turns, B = field, A = area, ω = angular frequency of rotation.
10.LC Oscillation Angular Frequency
$ω = \frac{1}{L C}$
Natural angular frequency of undamped LC circuit. Analogous to √(k/m) in SHM.
11.Charge in LC Circuit
$q (t) = q_{0} cos (ω t)$
Undamped harmonic; energy oscillates between C (electric) and L (magnetic).
12.Coefficient of Coupling
$k = \frac{M}{L _{1} L _{2}}$
0 ≤ k ≤ 1. k = 1 for perfect coupling (ideal transformer).