Electromagnetic Induction — Complete Formula

Magnetic Flux

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Magnetic Flux	[\Phi = BA\cos\theta]	[\Phi] = flux, [B] = magnetic field, [A] = area, [\theta] = angle	Wb	Field through surface ⭐

💡 Memory Hint:
Flux = number of field lines passing

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Induced EMF	[\mathcal{E} = -\dfrac{d\Phi}{dt}]	[\mathcal{E}] = emf	V	Rate of change of flux ⭐
Multiple Turns	[\mathcal{E} = -N\dfrac{d\Phi}{dt}]	[N] = number of turns	V	Coil case ⭐

💡 Memory Hint:
Changing flux → induced emf

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Direction	Opposes change in flux	—	—	Negative sign meaning ⭐

💡 Memory Hint:
Nature opposes change (not cause)

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Motional EMF	[\mathcal{E} = Blv]	[l] = length, [v] = velocity	V	Moving conductor ⭐
General Form	[\mathcal{E} = \int (\vec{v} \times \vec{B}) \cdot d\vec{l}]	—	V	Advanced use

💡 Memory Hint:
Motion in magnetic field → emf generated

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Current	[I = \dfrac{\mathcal{E}}{R}]	[R] = resistance	A	Ohm’s law applies ⭐

💡 Memory Hint:
EMF drives current through resistance

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Inductance	[L = \dfrac{\Phi}{I}]	[L] = inductance	H	Property of coil ⭐
Induced EMF	[\mathcal{E} = -L\dfrac{dI}{dt}]	—	V	Self induction ⭐

💡 Memory Hint:
Changing current → opposes itself

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Mutual Inductance	[M = \dfrac{\Phi_2}{I_1}]	—	H	Between two coils ⭐
Induced EMF	[\mathcal{E} = -M\dfrac{dI}{dt}]	—	V	Due to other coil

💡 Memory Hint:
One coil affects another coil

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Energy	[U = \dfrac{1}{2}LI^2]	—	J	Magnetic energy ⭐

💡 Memory Hint:
Inductor stores energy in magnetic field

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Induced EMF	[\mathcal{E} = NBA\omega \sin(\omega t)]	[N] = turns, [A] = area, [\omega] = angular speed	V	Alternating emf ⭐
Maximum EMF	[\mathcal{E}_{max} = NBA\omega]	—	V	Peak value

💡 Memory Hint:
Rotating coil → AC produced

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Eddy Currents	Circulating currents	—	—	Induced in bulk conductor ⭐
Power Loss	Depends on material	—	—	Causes heating ⚠️

💡 Memory Hint:
Eddy currents → energy loss (heating)

Concept	Formula	Symbols Meaning	SI Units	Key Notes
Flux	[\Phi = BA\cos\theta]	—	Wb	Base concept
Faraday Law	[\mathcal{E} = -\dfrac{d\Phi}{dt}]	—	V	Core formula ⭐
Motional EMF	[\mathcal{E} = Blv]	—	V	Moving rod ⭐
Inductor Energy	[U = \dfrac{1}{2}LI^2]	—	J	Energy storage

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