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Chapter 05 · Part V · Electromagnetism
Revised on ____________________

Chapter 05 · Electromagnetic Induction

Change the flux and the circuit fights back

sheets
diagrams
results

Formulas and conditions only — no derivations, no solved numbers. The diagrams are the reader's own.

Flux and Faraday's law

IT IS THE RATE, NOT THE VALUE

I.Magnetic flux Φ = B·A = B A cos θ weber

II.Faraday's law ℰ = − N dΦdt

III.Lenz's law the minus sign the induced effect opposes the change

IV.Charge moved q = N ΔΦR independent of how fast

V.Rotating coil ℰ = N B A ω sin ω t peak N B A ω

VI.Three ways to induce change B, change A, or rotate

VII.Eddy currents induced loops in a solid conductor braking, induction heating

VIII.Laminations cut the eddy paths, cut the loss

Lenz's law is conservation of energy wearing a minus sign. Whatever you do to the flux, the induced current arranges to make you work for it.

THE ROD, THE RAILS, THE RESISTOR

I.Straight rod ℰ = B ℓ v all three mutually perpendicular

II.Current I = B ℓ vR

III.Retarding force F = B² ℓ² vR ∝ v, so v decays exponentially

IV.Power P = B² ℓ² v²R mechanical in, electrical out

V.Rotating rod ℰ = 12 B ω ℓ²

VI.Terminal velocity v = m g RB² ℓ² a falling loop or rod

III

THE CIRCUIT'S OWN INERTIA

I.Self-inductance Φ = L I , ℰ = − L dIdt

II.Solenoid L = μ₀ n² A ℓ ∝ N², not N

III.Energy stored U = 12 L I²

IV.Energy density u = B²2 μ₀

V.Mutual inductance ℰ₂ = − M dI₁dt M₁₂ = M₂₁, always

VI.Coupling M = k √(L₁ L₂) k ≤ 1

VII.In series L = L₁ + L₂ ± 2M

VIII.In parallel 1L = 1L₁ + 1L₂ no coupling

τ = L/R, AND √(LC)

I.Growth I = ℰR (1 − e^−Rt/L) 63 % at t = L/R

II.Decay I = I₀ e^−Rt/L

III.At t = 0 an inductor is an open circuit at t = ∞, a plain wire

IV.LC oscillation ω = 1√(L C)

V.Its exchange 12 L I² ⇄ Q²2C like a mass on a spring

VI.Charge q = Q₀ cos ω t

FOUR ERRORS, EVERY YEAR

Where marks are lost in this chapter

1Reading a large flux as a large emf. Only the rate of change induces; steady flux induces nothing.

2Dropping Lenz's minus sign and getting the induced current's direction backwards.

3Taking L ∝ N for a solenoid. It goes as N² — double the turns and the inductance quadruples.

4Letting the current in an inductor jump. It is continuous: at switch-on I = 0, at switch-off it decays.