Class 12 · Chapter 6
Overview, notes, short notes, formula sheet, daily practice problems, previous year questions, and videos for this chapter — all in one place.
14 formulas across 4 topics in Electromagnetic Induction.
Updated 2026-07-09 · v1.0.0
A changing magnetic flux through a loop induces an EMF — the size of that EMF depends only on how fast the flux changes, not on the flux itself.
Φ = B·A = BA cosθ
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| Φ | magnetic flux | Wb (weber) | [ML²T⁻²A⁻¹] |
| B | magnetic field | T | [MT⁻²A⁻¹] |
| A | area of the surface | m² | [L²] |
| θ | angle between B and the area normal | rad | [M⁰L⁰T⁰] |
Valid when
ε = −N (dΦ/dt)
The negative sign is Lenz's law built in — the induced EMF always opposes the change producing it
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| ε | induced EMF | V | [ML²T⁻³A⁻¹] |
| N | number of turns in the coil | dimensionless | [M⁰L⁰T⁰] |
Valid when
Common mistakes
Worth remembering
A conductor moving through a magnetic field is a special case of Faraday's law — the Lorentz force on free charges inside the moving conductor does the work of separating charge.
ε = Bvl
Force per unit charge on free electrons in the rod is qv×B; integrating along the rod's length gives ε = Bvl
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| v | speed of the rod, perpendicular to both B and the rod | m/s | [LT⁻¹] |
| l | length of the rod | m | [L] |
Valid when
ε = ½ B ω l²
Integrating ε = ∫Bωr dr from 0 to l, since each element's speed is ωr
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| ω | angular speed of rotation | rad/s | [T⁻¹] |
Valid when
Common mistakes
ε = ε₀ sin(ωt) , ε₀ = NBAω
Φ = BA cos(ωt) for a coil rotating at constant ω; ε = −N dΦ/dt gives the sinusoidal EMF
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| ε₀ | peak (maximum) EMF | V | [ML²T⁻³A⁻¹] |
Valid when
Inductance measures a circuit's opposition to a CHANGING current — it plays the same conceptual role for current change that capacitance plays for charge storage.
Φ = LI , ε = −L (dI/dt)
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| L | self-inductance of the coil | H (henry) | [ML²T⁻²A⁻²] |
Valid when
L = μ₀ n² A l = μ₀N²A/l
Φ = B(nl·A) with B = μ₀nI inside the solenoid, then L = Φ/I = μ₀n²Al
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| n | turns per unit length | turns/m | [L⁻¹] |
| l | length of the solenoid | m | [L] |
Valid when
Φ₂ = MI₁ , ε₂ = −M (dI₁/dt)
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| M | mutual inductance between the two coils | H | [ML²T⁻²A⁻²] |
Valid when
M = μ₀N₁N₂A / l
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| N₁, N₂ | total turns of the two coils | dimensionless | [M⁰L⁰T⁰] |
Valid when
U = ½ L I²
U = ∫₀^I L I' dI', the work done building up the current against the self-induced back-EMF
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| U | energy stored in the magnetic field | J | [ML²T⁻²] |
Valid when
u = B² / (2μ₀)
U/(volume of solenoid) using U = ½LI² and L, B for a solenoid
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| u | energy per unit volume | J/m³ | [ML⁻¹T⁻²] |
Valid when
An inductor resists sudden current changes — connecting or disconnecting an LR circuit produces the same exponential growth/decay shape seen in RC circuits, but for current instead of charge.
τ = L / R
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| τ | time constant | s | [T] |
| R | resistance in the circuit | Ω | [ML²T⁻³A⁻²] |
Valid when
I(t) = I₀ (1 − e^(−t/τ))
Kirchhoff's voltage law: ε = IR + L(dI/dt), solved as a first-order ODE
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| I₀ | final steady-state current = ε/R | A | [A] |
Valid when
I(t) = I₀ e^(−t/τ)
Kirchhoff's voltage law with no source: L(dI/dt) + IR = 0
Valid when
Boards commonly ask to sketch and compare LR growth/decay against RC charging/discharging — the mathematical shape is identical, only the physical quantity (current vs. charge) differs.
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