Quick Revision Notes

Class 12 Physics - Electromagnetic Induction (EMI)

MP Board

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1. Introduction & Basic Concepts

• Electromagnetic Induction: The phenomenon of generating an electric current in a circuit by changing the magnetic flux linked with it.
• Magnetic Flux ($\Phi_B$): The total number of magnetic field lines passing normally through a given surface area.
  • Formula: Φ_B = B · A = B A cos(θ)
  • Unit: Weber (Wb) or Tesla-meter² ($\text{T}\cdot\text{m}^2$)
  • Dimension: [M^1 L^2 T^-2 A^-1]
  • It is a scalar quantity.

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2. Faraday’s Laws of Electromagnetic Induction

• First Law: Whenever the magnetic flux linked with a closed circuit changes, an electromotive force (emf) is induced in the circuit. It lasts only as long as the change in magnetic flux continues.
• Second Law: The magnitude of the induced emf is directly proportional to the rate of change of magnetic flux linked with the circuit.
  • Formula: e = - (dΦ_B) / (dt)
  • For a coil of $N$ turns: e = - N · (dΦ_B) / (dt)

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3. Lenz’s Law

• Statement: The direction of the induced emf or current is such that it opposes the very cause (the change in magnetic flux) that produces it.
• Conservation: Lenz's law is based on the Law of Conservation of Energy.
• Formula: e = - (dΦ_B) / (dt) (The negative sign indicates opposition).

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4. Motional Electromotive Force (Motional EMF)

When a straight conductor of length $l$ moves with velocity $v$ perpendicular to a uniform magnetic field $B$:

• Induced EMF: e = B · l · v
• Induced Current ($I$): I = (B l v) / R (where $R$ is the resistance of the circuit)
• Magnetic Force ($F$): F = I l B = (B^2 l^2 v) / R
• Power Delivered ($P$): P = (B^2 l^2 v^2) / R

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5. Eddy Currents

• Definition: Circulating currents induced in bulk pieces of conductors when the magnetic flux linked with them changes. They are also known as Foucault currents.
• Applications: Electromagnetic damping, induction furnaces, magnetic braking in trains, and speedometers.
• Minimization: Eddy currents cause unwanted heat and energy loss. They are minimized by using laminated cores in transformers and dynamos.

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6. Inductance

A. Self-Induction ($L$)

The property of a coil by virtue of which it opposes any change in the strength of current flowing through it by inducing an emf in itself.

• Magnetic flux linked is proportional to current: NΦ_B ∝ I $\Rightarrow$ NΦ_B = L I
• Self-Inductance ($L$): L = (NΦ_B) / I
• Induced EMF: e = - L · (dI / dt)
• Unit of Inductance: Henry (H) or $\text{V}\cdot\text{s}\cdot\text{A}^{-1}$
• Self-Inductance of a Long Solenoid: L = (μ_0 μ_r N^2 A) / l (where $N$ = total turns, $A$ = area, $l$ = length)

B. Mutual Induction ($M$)

The phenomenon by virtue of which an opposing emf is induced in a secondary coil due to a change in current in the primary coil.

• Total flux linked with secondary is proportional to current in primary: N_s Φ_s ∝ I_p $\Rightarrow$ N_s Φ_s = M I_p
• Mutual Inductance ($M$): M = (N_s Φ_s) / (I_p)
• Induced EMF in Secondary: e_s = - M · (dI_p / dt)
• Mutual Inductance of Two Long Coaxial Solenoids: M = (μ_0 N_1 N_2 A) / l

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7. Energy Stored in an Inductor

• When a current $I$ flows through an inductor of self-inductance $L$, the magnetic potential energy stored in it is:
  • Formula: U = (1/2) L I^2
• Magnetic Energy Density ($u_B$): Energy stored per unit volume in a magnetic field.
  • Formula: u_B = B^2 / (2 μ_0)

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8. AC Generator (Dynamo)

• Principle: Based on Electromagnetic Induction. It converts mechanical energy into electrical energy.
• Instantaneous Induced EMF: e = NBAω sin(ωt) (where $N$ = number of turns, $B$ = magnetic field, $A$ = area of coil, $\omega$ = angular velocity)
• Peak Value of EMF ($e_0$): e_0 = N B A ω
• Therefore, e = e_0 sin(ωt)

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Quick Tip for MP Board Exams:

• Always write proper SI units with your final answers (e.g., Weber for Flux, Henry for Inductance, Volt for EMF).
• State Lenz's Law clearly mentioning the Conservation of Energy for 2-3 mark questions.
• Derivations for Motional EMF and Self/Mutual Inductance of a Solenoid are frequently asked in the 4-5 mark sections.