Physics by Lamhi: Not Your Boring Physics

CLASS 12 · CHAPTER 6 · ELECTROMAGNETISM

QUICK REVISION

Electromagnetic Induction

Every key result from this chapter, boxed and ready for a last look before the exam. No derivations here, just what to recall and when to use it — for the full explanation, see the detailed notes.

1. Magnetic Flux

Flux
Φ=B⃗⋅A⃗=BAcos⁡θ\Phi = \vec{B}\cdot\vec{A} = BA\cos\theta

Max at θ = 0° (field ⊥ surface), zero at θ = 90° (field in the plane of the surface).

2. Faraday's Law

Induced EMF
ε=−NdΦdt\varepsilon = -N\dfrac{d\Phi}{dt}

Depends only on the rate of change of flux, not the flux itself, and not on what causes the change.

3. Lenz's Law

  1. Induced current always opposes the change in flux that produced it (the minus sign above).
  2. This is energy conservation, restated as a direction rule, not an independent assumption.

4. Motional EMF

EMF of a rod sliding at v, length L, field B
ε=BLv,I=εR=BLvR\varepsilon = BLv, \qquad I = \dfrac{\varepsilon}{R} = \dfrac{BLv}{R}

EMF exists the instant the rod moves, regardless of whether the circuit is closed; only I needs a closed circuit.

5. Retarding Force & Power — the exam trap

Force (linear in v) and power (quadratic in v)
F=BIL=B2L2vR,P=Fv=I2R=B2L2v2RF = BIL = \dfrac{B^2L^2v}{R}, \qquad P = Fv = I^2R = \dfrac{B^2L^2v^2}{R}
  1. F ∝ v: double the speed, the retarding force you push against only doubles.
  2. P ∝ v²: double the speed, the power you must supply quadruples, not doubles.
  3. Always check Fv=I2RFv=I^2R: mechanical work in must equal heat dissipated in R exactly.

See it live: interactive motional EMF simulation →

6. Self & Mutual Inductance

Self-inductance
ε=−LdIdt\varepsilon = -L\dfrac{dI}{dt}
Mutual inductance
ε2=−MdI1dt\varepsilon_2 = -M\dfrac{dI_1}{dt}

L: a coil resisting change in its own current. M: one coil inducing EMF in a separate coil (transformers).

7. Energy Stored in an Inductor

Stored energy
U=12LI2U = \dfrac{1}{2}LI^2

Magnetic analogue of U = ½CV² for a capacitor.

Full derivations and worked examples: detailed notes →