Electromagnetism and Wave Physics: Key Concepts and Formulas

What is the formula for magnetic flux?

Φ = B A cosθ

What causes induced emf?

Changing magnetic flux

What is Faraday's Law?

ℰ = −N dΦ/dt

What does the negative sign in Faraday's Law indicate?

Lenz's Law → opposes change in flux

What is the formula for motional emf?

ℰ = Bℓv

Can emf exist if flux is zero?

Yes, if flux is changing

When is flux maximum and when is emf maximum?

Flux max when flat; emf max when edge-on

What does an inductor resist?

Change in current

What is the formula for inductor emf?

ℰ = −L dI/dt

What is the energy stored in an inductor?

U = ½LI²

What is the initial current in an RL circuit when the switch is closed?

Current = 0

What happens in an RL circuit after a long time?

Acts like wire → I = E/R

What is the RL time constant?

τ = L/R

What happens to energy in an LC circuit?

Energy oscillates (electric ↔ magnetic)

What is the formula for LC frequency?

ω = √(1/LC)

What is the resonance condition?

XL = XC

Why is current maximum at resonance?

Inductive + capacitive reactance cancel

What is the formula for inductive reactance?

XL = ωL

What is the formula for capacitive reactance?

XC = 1/(ωC)

What is the formula for impedance?

Z = √((XL − XC)² + R²)

What is the formula for current amplitude?

I₀ = V₀ / Z

What is the physical idea of an inductor?

Acts like inertia for current

What is the phase relationship for a resistor?

Voltage and current in phase

What is the phase relationship for a capacitor?

Current leads voltage

What is the phase relationship for an inductor?

Current lags voltage

What does resonance mean in a circuit?

Circuit behaves purely resistive

What is the formula for resonant frequency?

ω₀ = √(1/LC)

What does average power depend on?

Phase difference

When is power maximum in a circuit?

At resonance

What is the transformer voltage ratio?

Vs/Vp = Ns/Np

What is the transformer current ratio?

Is/Ip = Np/Ns

What is the power in a transformer?

VpIp = VsIs

Why is high voltage transmission used?

Lower current → less power loss

What is an electromagnetic wave?

Oscillating electric and magnetic fields

What is the direction of an electromagnetic wave?

E × B

What is the relationship between E and B in EM waves?

B = E / c

What is the formula for wave speed?

c = λf

What is the formula for angular frequency?

ω = 2πf

What is the formula for wave number?

k = 2π/λ

What is the electromagnetic wave equation?

E = E₀ sin(kx − ωt)

What is the energy density of an electric field?

u = ½ε₀E²

What is the energy density of a magnetic field?

u = B²/(2μ₀)

What is the Poynting vector?

S = (1/μ₀)(E × B)

What is the formula for intensity?

I = ½ε₀cE₀²

How does intensity relate to amplitude?

I ∝ E²

What is the radiation pressure for absorbed waves?

P = I/c

What is the radiation pressure for reflected waves?

P = 2I/c

Do electromagnetic waves need a medium?

No

What creates electromagnetic waves?

Accelerating charges

What type of wave are electromagnetic waves?

Transverse

What happens if frequency increases?

Wavelength decreases

What happens if amplitude doubles?

Intensity increases by 4×