CBSE · Class 12 · Physics · Chapter 6

Electromagnetic Induction — Formula Sheet

Board Formulas

12 formulas

1.Magnetic Flux
$Φ = B \cdot A = B A cos θ$
$Φ$ : Magnetic flux (Wb = T·m²) · $θ$ : Angle between B and area vector
Flux is maximum when B is normal to the surface (θ = 0), zero when parallel.
2.Faraday's Law of Induction★
$ε = - N \frac{d Φ}{d t}$
$ε$ : Induced EMF (V) · $N$ : Number of turns · $d Φ/ d t$ : Rate of change of flux (Wb/s)
Induced EMF is proportional to the rate of change of flux linkage.
3.Lenz's Law★
$ε = - \frac{d Φ}{d t}$
Induced current flows in a direction that opposes the change in flux — direct consequence of energy conservation.
4.Motional EMF★
$ε = B Lv$
EMF induced in a conductor of length L moving with velocity v perpendicular to B.
5.Self-Induced EMF
$ε = - L \frac{d I}{d t}$
$L$ : Self-inductance (H = Wb/A) · $d I / d t$ : Rate of change of current (A/s)
A changing current in a coil induces an EMF in the same coil (opposing the change).
6.Self-Inductance of a Solenoid★
$L = μ_{0} n^{2} A l = \frac{μ _{0} N ^{2} A}{l}$
Depends only on geometry and the medium. Larger N, area, or ferromagnetic core → higher L.
7.Mutual Inductance
$ε_{2} = - M \frac{d I _{1}}{d t}$
$M$ : Mutual inductance (H) · $I_{1}$ : Current in primary coil (A)
EMF in coil 2 caused by changing current in coil 1. M depends on geometry and relative position.
8.Mutual Inductance of Two Coaxial Solenoids
$M = μ_{0} n_{1} n_{2} A l$
For an inner solenoid completely surrounded by an outer solenoid.
9.Energy Stored in an Inductor
$U = \frac{1}{2} L I^{2}$
Energy is stored in the magnetic field of the inductor.
10.Magnetic Energy Density
$u_{B} = \frac{B ^{2}}{2 μ _{0}}$
Energy per unit volume stored in a magnetic field. Analogue of ½ε_0 E².
11.AC Generator EMF
$ε = ε_{0} sin (ω t), ε_{0} = N B A ω$
Peak EMF depends on turns, area, field and angular speed.
12.Series/Parallel Inductors (no mutual coupling)
$L_{ser i es} = L_{1} + L_{2}, \frac{1}{L _{p a r a l l e l}} = \frac{1}{L _{1}} + \frac{1}{L _{2}}$
Add like resistors — direct sum in series, reciprocal sum in parallel.