Electromagnetic Induction Class 12 Physics Formula Sheet 2026-27 | Important Formulas

CBSE Class 12 PhysicsChapter 62026–27Quick Revision

Electromagnetic Induction Class 12 Physics — Formula Sheet + Quick Revision

A compact, syllabus-aware Electromagnetic Induction Class 12 Physics formula sheet for CBSE 2026–27, covering magnetic flux, Faraday’s law, Lenz’s law, induced EMF and current, motional EMF, rotating-rod EMF, self-induction, mutual induction, energy stored in an inductor, important units, formula selection and exam traps.

2026–27 syllabus boundary: The official CBSE curriculum places electromagnetic induction, Faraday’s laws, induced EMF and current, Lenz’s law, self-induction and mutual induction in Chapter 6. AC generator and transformer are in Chapter 7: Alternating Current, so they are not included in this Chapter 6 core formula sheet. Unit IV carries 18 marks collectively for Chapters 6 and 7; CBSE does not assign a fixed standalone mark allocation to Chapter 6.

How to use this page: First learn what each formula means and when it applies. Then use the Chapter 6 Numericals and PYQs to practise selecting the correct relation. Do not treat a formula as valid without checking the geometry, sign convention, circuit condition and units.

Formula-at-a-glance: Φ_B = BA cosθ  |  ε = −N dΦ_B/dt  |  ε_avg = −NΔΦ_B/Δt  |  ε = Bℓv  |  ε = −L dI/dt  |  U = ½LI²  |  ε₂ = −M dI₁/dt
For quick board revision, connect every formula to the physical quantity that is changing.

Chapter 6 formula map: Start with flux → Faraday → Lenz, then move to motional EMF → induced charge → self-induction → mutual induction → magnetic energy. This sequence mirrors the way most Chapter 6 numerical and reasoning problems are solved: identify the changing flux/current first, then choose the governing relation.

High-intent revision topic	Core formula	What to check before using it
Magnetic flux	ΦB = BA cosθ	θ is with the area vector; convert units.
Faraday’s law	ε = −N dΦB/dt	Use N turns and the correct rate of flux change.
Motional EMF	ε = Bℓv	Standard perpendicular geometry.
Self-induction	ε = −L dI/dt	Changing current in the same coil.
Mutual induction	ε2 = −M dI1/dt	Changing current in one coupled coil.
Energy in inductor	U = ½LI²	Use current I and inductance L in SI units.

1. Magnetic Flux2. Faraday’s Law3. Lenz’s Law4. EMF & Current 5. Motional EMF6. Induced Charge7. Self-Induction8. Mutual Induction 9. Energy10. Units11. Exam Traps12. Self-Check

1. Magnetic Flux — The Starting Point

Uniform magnetic field through a plane surface

Φ_B = B A cos θ

Φ_B = magnetic flux, B = magnetic field, A = area, and θ = angle between B and the area vector (normal to the surface). SI unit: weber (Wb).

Vector form

Φ_B = B · A

Use the dot product when the field and area are treated as vectors. The angle convention is the same: measure θ from the surface normal, not from the plane itself.

Maximum flux:
θ = 0° → Φ_B = BA

Zero flux:
θ = 90° → Φ_B = 0

Important:
A constant magnetic field through a stationary fixed loop does not by itself imply induced EMF.

What can change flux?
B, A, θ, or any combination of them.

Exam trap: In Φ = BA cosθ, θ is measured between B and the area vector. If a question gives the angle between B and the plane, convert it before using the cosine relation.

2. Faraday’s Laws of Electromagnetic Induction

Instantaneous induced EMF — N turns

ε = −N dΦ_B/dt

The magnitude of induced EMF depends on the rate of change of magnetic flux linkage. The negative sign represents Lenz’s law.

Average induced EMF

ε_avg = −N ΔΦ_B/Δt

Use this for a finite interval when the total flux change and time interval are given. For magnitude-only questions, |ε_avg| = N|ΔΦ|/Δt.

Flux linkage

Flux linkage = NΦ_B

If each of N turns links the same flux Φ_B, the total flux linkage is NΦ_B. Faraday’s law can therefore be viewed as the rate of change of flux linkage.

Graph cue: In a Φ–t graph, the slope gives dΦ/dt. For an N-turn coil, induced-EMF magnitude is N times the magnitude of that slope.

3. Lenz’s Law — Direction and Energy

Lenz’s law: the induced effect opposes the change in magnetic flux that produces it.

The minus sign in Faraday’s law is the mathematical expression of this direction rule. The induced current does not simply “oppose the magnetic field”; it opposes the change in flux.

Flux increasing:
Induced magnetic effect opposes the increase.

Flux decreasing:
Induced magnetic effect supports the original field to oppose the decrease.

Magnet approaching a coil:
First identify the pole/field change at the coil, then use Lenz’s law to determine the induced face/current direction.

Energy check:
If the induced effect reinforced the change automatically, energy could be produced without the required external work. Lenz’s law prevents that.

4. Induced EMF and Induced Current

Ohm’s-law form for a simple resistive closed circuit

I = ε/R

For a circuit whose effective resistance is R and where the simple resistive model applies, induced current magnitude is |I| = |ε|/R.

Combined Faraday + resistance relation

I = −(N/R) dΦ_B/dt

This is useful when a question asks directly for induced current from the rate of flux change. Direction still requires Lenz’s-law reasoning.

Remember: A changing flux can induce EMF even if the circuit is open. A sustained conduction current requires a closed conducting path.

5. Motional EMF

Standard moving-rod case

ε = Bℓv

Use for the standard arrangement in which a rod of length ℓ moves with speed v perpendicular to a magnetic field B, with the geometry producing the usual Bℓv result.

General geometry cue

ε = Bℓv sinα

For the common straight-rod geometry, α is the relevant angle between the velocity and magnetic-field directions. Check the actual arrangement before simplifying to Bℓv.

Rotating rod — standard radial case

ε = ½Bωℓ²

For a conducting rod of length ℓ rotating about one end with angular speed ω in a uniform magnetic field perpendicular to the plane of rotation. Use only for the stated geometry.

Why Bℓv is not enough here

v = ωr

Different points of a rotating rod have different linear speeds. Integrating the small EMF contributions gives the ½Bωℓ² result for the standard radial geometry.

Problem-solving sequence: identify the moving conductor → identify B, ℓ and v → check the geometry → calculate EMF magnitude → use the appropriate direction rule (for example, magnetic force on charges/Lorentz-force reasoning or Lenz’s law in a complete loop).

Rotating-conductor caution: Do not automatically use ε = Bℓv for every rotating-rod problem. When speed varies along the conductor, integrate or use the appropriate geometry-specific expression. The formula sheet is a revision map, not permission to ignore the setup.

6. Induced Charge

Total charge transferred in a simple closed circuit

q = N|ΔΦ_B| / R

For a simple circuit of constant resistance R, integrating I = ε/R gives the total charge transferred for a flux change. The result does not depend on how quickly the flux change occurs.

Fast reasoning: Same N, same |ΔΦ| and same R → same total induced charge, even if one flux change happens faster than another. Faster change produces larger instantaneous EMF/current, but not necessarily more total charge.

7. Useful Motional-EMF Results for Numericals

Magnetic force on a moving conducting loop

F = B²ℓ²v/R

For the standard sliding-rod/closed-loop arrangement with resistance R, uniform B and constant speed v. The external force required to maintain constant speed has the same magnitude.

Electrical/thermal power in the loop

P = v²B²ℓ²/R

For the same ideal arrangement. It is also consistent with P = I²R when I = Bℓv/R.

Scope note: These two relations are useful for standard Chapter 6 motional-EMF numericals found in NCERT-aligned revision material. They are application formulas, so always confirm that the stated geometry matches the standard sliding-rod setup.

8. Self-Induction and Self-Inductance

Self-induced EMF

ε = −L dI/dt

L is self-inductance. The induced EMF opposes the change in current in the same coil.

Flux-linkage definition of self-inductance

NΦ_B = LI

For the ideal linear case, flux linkage is proportional to current. This relation is especially useful for understanding what the coefficient L represents.

Long air-core solenoid

L = μ₀N²A/ℓ

Use for a long air-core solenoid under the standard ideal approximation. L increases with N² and A, and decreases with length ℓ.

Scaling rule

L ∝ N²A/ℓ

Excellent for comparison questions: doubling N makes L four times larger; doubling A doubles L; doubling ℓ halves L, provided the other quantities remain unchanged.

Unit: SI unit of self-inductance is henry (H). Do not confuse inductance L with magnetic flux Φ or magnetic field B.

9. Mutual Induction and Mutual Inductance

Mutual-induced EMF in coil 2

ε₂ = −M dI₁/dt

A changing current in coil 1 induces EMF in coupled coil 2. M is the mutual inductance of the pair.

Flux-linkage relation

N₂Φ₂₁ = MI₁

For the ideal linear coupled-coil model, mutual inductance relates the current in the primary coil to flux linkage in the secondary coil.

Ideal coaxial long-solenoid arrangement

M = μ₀N₁N₂A/ℓ

Use for the standard ideal geometry of long coaxial solenoids with common cross-sectional area A and length ℓ.

Comparison with self-inductance

M ∝ N₁N₂A/ℓ

Changing either coil’s number of turns changes M proportionally, unlike self-inductance which depends on the square of the turns of its own coil in the ideal solenoid model.

Self vs mutual: Self-induction → changing current in a coil induces EMF in the same coil. Mutual induction → changing current in one coil induces EMF in a different coupled coil.

10. Energy Stored in an Inductor

Magnetic energy stored

U = ½LI²

Energy stored in an inductor carrying current I. SI unit: joule (J).

Scaling

U ∝ LI²

If L is fixed, doubling I makes stored energy four times larger. If I is fixed, doubling L doubles the stored energy.

Magnetic energy density — useful extension

u_B = B²/(2μ₀)

Energy stored per unit volume of a magnetic field in vacuum/air under the standard ideal-field treatment. SI unit: J m⁻³.

Common numerical pattern: Questions may compare two coils or two current values rather than asking for a direct substitution. Use the proportional relation first, then calculate only if necessary.

11. Units, Symbols and Dimensions at a Glance

Quantity	Symbol	SI unit	Quick note
Magnetic flux	ΦB	weber (Wb)	1 Wb = 1 V·s
Magnetic field	B	tesla (T)	Flux density
Area	A	m²	Convert cm² to m² in SI calculations
Induced EMF	ε	volt (V)	Magnitude is often requested; sign carries direction information
Current	I	ampere (A)	Use I = ε/R for a simple resistive model
Resistance	R	ohm (Ω)	Check total/effective resistance
Self-inductance	L	henry (H)	1 H = 1 V·s/A
Mutual inductance	M	henry (H)	Same SI unit as L
Energy	U	joule (J)	U = ½LI²
Turns	N, N1, N2	dimensionless	Count of coil turns

12. Formula Selection Guide — Which Formula Should I Use?

If the question gives…	Think first	Use
B, A and angle	Magnetic flux	Φ = BA cosθ
Change in flux and time	Average induced EMF	|ε| = N|ΔΦ|/Δt
Flux as a function of time	Instantaneous EMF	ε = −N dΦ/dt
Induced EMF and resistance	Induced current	I = ε/R
Moving rod with standard perpendicular geometry	Motional EMF	ε = Bℓv
Flux change and circuit resistance	Total induced charge	q = N|ΔΦ|/R
Change in current in the same coil	Self-induced EMF	ε = −L dI/dt
Long solenoid geometry	Self-inductance	L = μ₀N²A/ℓ
Current and self-inductance	Stored energy	U = ½LI²
Change in primary current and coupled secondary coil	Mutual induction	ε₂ = −M dI₁/dt
Two coupled long coaxial solenoids	Mutual inductance	M = μ₀N₁N₂A/ℓ

13. Common Exam Traps

• Trap 1: The angle in Φ = BA cosθ is measured from the area vector, not the plane.
• Trap 2: Lenz’s law opposes the change in flux, not simply the magnetic field itself.
• Trap 3: A changing flux can induce EMF in an open circuit; current requires a closed conducting path.
• Trap 4: Do not use ε = Bℓv blindly. Check the geometry and whether B, ℓ and v have the required orientation.
• Trap 5: Self-induction and mutual induction are different: same coil versus coupled different coil.
• Trap 6: For long-solenoid inductance, convert all lengths and areas to SI units before substitution.
• Trap 7: In proportional questions, remember L ∝ N²A/ℓ and U ∝ LI².
• Trap 8: AC generator and transformer are Chapter 7 topics in the current CBSE 2026–27 syllabus; do not mix them into Chapter 6 core revision.

14. One-Minute Concept Map

Concept	One-line memory cue
EMI	Changing magnetic flux linkage produces induced EMF.
Flux	Φ = BA cosθ; θ is with the area vector.
Faraday	ε = −N dΦ/dt; rate of flux-linkage change controls EMF.
Lenz	Induced effect opposes the change that caused it.
Motional EMF	A moving conductor in a magnetic field can develop EMF.
Self-induction	Changing current in a coil produces opposing EMF in the same coil.
Mutual induction	Changing current in one coil produces EMF in a coupled second coil.
Inductor energy	U = ½LI².

15. 20-Minute Quick Revision Plan

1. 3 minutes: revise Φ = BA cosθ, area-vector angle and flux-change causes.
2. 4 minutes: revise Faraday’s law, average EMF, flux linkage and Lenz’s law.
3. 3 minutes: revise induced current, motional EMF and induced charge.
4. 4 minutes: revise self-induction, L = μ₀N²A/ℓ and ε = −L dI/dt.
5. 3 minutes: revise mutual induction, M and ε₂ = −M dI₁/dt.
6. 3 minutes: revise U = ½LI², units and the exam traps.

16. 60-Second Self-Check

• Can I calculate magnetic flux and identify the correct angle?
• Can I distinguish average EMF from instantaneous EMF?
• Can I explain the minus sign in Faraday’s law using Lenz’s law?
• Can I decide when a changing flux produces current rather than only EMF?
• Can I select Bℓv only when the geometry supports it?
• Can I distinguish self-induction from mutual induction?
• Can I use L = μ₀N²A/ℓ and U = ½LI² correctly?
• Can I identify Chapter 7 topics that should not be mixed into Chapter 6?

17. Continue Your Chapter 6 Preparation

Chapter 6 Notes Important Questions MCQs Numericals Case-Based Questions Assertion–Reason PYQs with Solutions Chapter 5 Notes — Previous Chapter

Official references: CBSE Physics Curriculum 2026–27 · CBSE Class XII 2026–27 SQP & Marking Scheme

Source note: This is an original Learn Revise Hub revision resource, not an official CBSE document. The 2026–27 chapter boundary follows the official CBSE Physics curriculum. Formula selection was cross-checked against current NCERT-aligned Class 12 revision references, while the official CBSE curriculum was used to keep Chapter 6 and Chapter 7 boundaries separate.