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Advanced Electromagnetism — Maxwell's Equations

Electrostatics, magnetostatics, and electromagnetic theory

F
field_lines_fl 25 terms Jan 10, 2026
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Terms 25

1
Gauss's Law (electric)
∮ E·dA = Q_enc/ε₀; total electric flux through closed surface equals enclosed charge / ε₀
2
Gauss's Law (magnetic)
∮ B·dA = 0; no magnetic monopoles; field lines always close
3
Faraday's Law
∮ E·dl = −dΦ_B/dt; changing magnetic flux induces EMF
4
Ampère-Maxwell Law
∮ B·dl = μ₀(I + ε₀ dΦ_E/dt); current and changing E field create B field
5
Electric Field (E)
Force per unit positive charge: E = F/q; from Coulomb's law: E = kq/r² r̂
6
Electric Potential (V)
Work per unit charge: V = kq/r; E = −∇V
7
Capacitance
C = Q/V; ability to store charge; parallel plate: C = ε₀A/d
8
Dielectric
Insulating material reducing E field inside capacitor; increases capacitance by factor κ
9
Magnetic Field (B)
Force on moving charge: F = qv×B; field of wire: B = μ₀I/2πr
10
Biot-Savart Law
dB = (μ₀/4π)(I dl×r̂)/r²; magnetic field from infinitesimal current element
11
Ampère's Law
∮ B·dl = μ₀I_enc; path integral of B equals μ₀ times enclosed current
12
Magnetic Flux (Φ_B)
Φ_B = ∫ B·dA; total magnetic field through a surface
13
Inductance (L)
L = NΦ_B/I; opposes changes in current; V_L = −L dI/dt
14
RL Circuit
Time constant τ = L/R; current rises as I = I₀(1 − e^(−t/τ)) when connected
15
LC Circuit
Oscillates at ω₀ = 1/√(LC); energy alternates between electric and magnetic
16
Electromagnetic Wave
Coupled oscillating E and B fields; propagates at c = 1/√(μ₀ε₀)
17
Poynting Vector (S)
S = (1/μ₀)(E×B); energy flux of EM wave; W/m²
18
Radiation Pressure
P = S/c for absorbed wave; EM waves carry momentum
19
Index of Refraction
n = c/v; ratio of speed of light in vacuum to speed in medium
20
Snell's Law
n₁ sin(θ₁) = n₂ sin(θ₂); governs refraction at interface
21
Total Internal Reflection
Occurs when θ > θ_c = arcsin(n₂/n₁); basis of optical fiber
22
Displacement Current
Maxwell's addition: ε₀ dΦ_E/dt; allows EM waves to propagate through vacuum
23
Lorentz Force
F = q(E + v×B); total electromagnetic force on a charged particle
24
Self-Inductance
EMF induced in a coil by its own changing current; opposes change (Lenz's law)
25
Mutual Inductance
EMF induced in secondary coil by changing current in primary; basis of transformer