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Electromagnetic Induction Class 12 Physics Notes

Complete, exam-ready notes on electromagnetic induction: magnetic flux, Faraday's laws, Lenz's law and energy conservation, motional EMF, self and mutual inductance, AC generators and the transformer — written for CBSE boards, JEE and NEET revision.

Class12SubjectPhysicsCoversCBSE · JEE · NEET

Written byDeep Narayan· Science & Mathematics EducatorReviewed byPushpanjali

What is electromagnetic induction in one line?

Electromagnetic induction is the production of an EMF (and current) in a conductor when the magnetic flux linked with it changes, as described by Faraday's law.

Magnetic Flux and Faraday's Law

Magnetic flux

Φ=BAcos⁡θ\Phi = BA\cos\theta

The magnetic flux through a surface is the product of the field, the area and the cosine of the angle between them. Its SI unit is the weber (Wb).

Faraday's law

ε=−dΦdt\varepsilon = -\frac{d\Phi}{dt}

The induced EMF equals the negative rate of change of magnetic flux. For N turns, ε=−NdΦdt\varepsilon = -N\frac{d\Phi}{dt}.

The minus sign is Lenz's law

The negative sign in Faraday's law reflects Lenz's law: the induced current opposes the change in flux that produces it. This is a manifestation of energy conservation.

Lenz's Law

Lenz's law

The direction of the induced current is such that it opposes the change in magnetic flux that induces it. Approaching a magnet, the loop repels; moving away, it attracts.

Induced field direction

If flux is increasing into a loop, the induced current produces a field out of the loop (opposing the increase). If flux decreases, the induced field reinforces the original field.

Motional EMF

Motional EMF

ε=B l v\varepsilon = B\,l\,v

When a conductor of length l moves with speed v perpendicular to a field B, a motional EMF of Blv is induced. The induced current flowing rounds a loop produces a force opposing the motion.

  • The motional EMF can be understood as the magnetic force on the free charges inside the moving conductor.
  • Rotating a rod of length l about one end in a field B induces
  • ε=12Bωl2\varepsilon = \frac{1}{2}B\omega l^2
  • .
ε=Blv,εrotating rod=12Bωl2\varepsilon = Blv,\quad \varepsilon_{\text{rotating rod}} = \frac{1}{2}B\omega l^2
Motional EMF formulas

Self and Mutual Inductance

Self inductance

L=NΦIL = \frac{N\Phi}{I}

Self inductance is the flux linked per unit current; the induced EMF is ε=−LdIdt\varepsilon = -L\frac{dI}{dt}. Energy stored in an inductor: U=12LI2U = \frac{1}{2}LI^2.

Mutual inductance

M=N2Φ2I1M = \frac{N_2\Phi_2}{I_1}

Mutual inductance links the flux in a secondary coil to the current in a primary: ε2=−MdI1dt\varepsilon_2 = -M\frac{dI_1}{dt}.

U=12LI2,ε2=−MdI1dtU = \frac{1}{2}LI^2,\quad \varepsilon_2 = -M\frac{dI_1}{dt}
Inductor energy and mutual EMF

AC Generator and Transformer

  • AC generator: a coil rotating in a magnetic field produces a sinusoidally varying EMF
  • ε=NBAωsin⁡ωt\varepsilon = NBA\omega\sin\omega t
  • .
  • Transformer: mutual inductance transfers energy between windings.
  • VsVp=NsNp\frac{V_s}{V_p} = \frac{N_s}{N_p}
  • .
  • Step-up transformers have more secondary turns; step-down have fewer.
  • Ideal transformer:
  • VpIp=VsIsV_p I_p = V_s I_s
  • (power conserved).
VsVp=NsNp,VpIp=VsIs\frac{V_s}{V_p} = \frac{N_s}{N_p},\quad V_p I_p = V_s I_s
Transformer relations

Solved Examples

Example: A 0.5 m0.5\,\text{m} conductor moves at 4 m/s4\,\text{m/s} perpendicular to a 0.2 T0.2\,\text{T} field. Find the motional EMF.

Solution: ε=Blv=0.2×0.5×4=0.4 V\varepsilon = Blv = 0.2\times0.5\times4 = 0.4\,\text{V}.

Revision

Key formulas at a glance

Memorise these before attempting numericals — most exam questions hinge on one of them.

Magnetic flux

Φ=BAcos⁡θ\Phi = BA\cos\theta

Faraday's law

ε=−dΦdt\varepsilon = -\frac{d\Phi}{dt}

Motional EMF

ε=Blv\varepsilon = Blv

Self inductance

ε=−LdIdt\varepsilon = -L\frac{dI}{dt}

Inductor energy

U=12LI2U = \frac{1}{2}LI^2

Transformer

VsVp=NsNp\frac{V_s}{V_p} = \frac{N_s}{N_p}

Exam tips

How this chapter is asked

Where this topic appears in CBSE, JEE Main and NEET papers.

  • Faraday's law: ε = −dΦ/dt.
  • Lenz's law: induced current opposes the flux change.
  • Motional EMF = Blv.
  • Energy in an inductor U = LI²/2.
  • Transformer: Vs/Vp = Ns/Np; power conserved.

FAQ

Common questions

What is Lenz's law?

The induced current opposes the change in flux that produces it — approaching a magnet, the loop repels; moving away, it attracts. It follows from energy conservation.

What is motional EMF?

The EMF induced when a conductor moves through a magnetic field, given by ε = Blv. It arises because the magnetic force drives free charges along the conductor.

How does a transformer work?

An alternating current in the primary winding creates a changing flux linked to the secondary, inducing an EMF. The voltage ratio equals the turns ratio Ns/Np.

What is self inductance?

The flux linked with a coil per unit current in itself; changes in current induce a back EMF ε = −L(dI/dt).

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Related notes

All Class 12 NotesClass 12 Moving Charges NotesClass 12 Magnetism and Matter NotesPhysics Tutor in Mohali

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