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Electromagnetism & Electronics

Faraday's Law of Induction

Maxwell's third equation stating that a time-varying magnetic flux through a closed conductive loop induces an electromotive force (EMF)…

E = -dΦ_B / dt, ∇ × E = -∂B/∂t V (Volts) Mathematical & Computational Physics

Fast Fourier Transform (FFT)

An efficient algorithm that computes the Discrete Fourier Transform (DFT) of a sequence in O(N log N) operations instead of O(N²).

Cooley-Tukey Divide-and-Conquer: O(N log N) vs O(N²) Computational FFT Algorithm Condensed Matter & Materials Physics

Fatigue

The progressive structural weakening and microcrack failure of a material subjected to repeated cyclic loading stresses below its ultimate…

Basquin's Relation: S_a = σ'_f (2 N_f)^b Cycles to Failure N_f Optics

Fermat's Principle

The fundamental principle stating that light traveling between two points follows the path that requires the stationary (usually minimum)…

Optical Path Length L = ∫ n(s) ds = extremum s (or m) Quantum & Atomic Physics

Fermi Energy

The highest occupied kinetic energy state of non-interacting fermions in a quantum system at absolute zero temperature (0 K).

E_F = (ℏ² / (2 m)) (3 π² n)^(2/3) eV or Joules Condensed Matter & Materials Physics

Fermi Level

The thermodynamic Fermi-Dirac chemical potential representing the energy level at which the probability of electron occupancy is exactly…

f(E) = 1 / (e^((E - E_F) / (k_B T)) + 1) eV (Chemical Potential) Astrophysics, Cosmology & Relativity

Fermi Paradox

The apparent contradiction between high probabilistic estimates for the existence of extraterrestrial civilizations and the complete lack…

Enrico Fermi: 'Where is everybody?' Astronomical Paradox Quantum & Atomic Physics

Fermions

Subatomic particles possessing half-integer intrinsic spin that obey Fermi-Dirac statistics and the Pauli Exclusion Principle.

Spin = ½, ³/₂, ⁵/₂... Dimensionless Particle Class Electromagnetism & Electronics

Ferromagnetism

A strong magnetic phenomenon in which atomic magnetic moments spontaneously align parallel into localized magnetic domains, producing…

μ_r ≫ 1 (μ_r ~ 1,000–100,000) Dimensionless Nuclear & Particle Physics

Feynman Diagram

Visual pictorial representations of mathematical expressions describing the quantum interaction and scattering behavior of subatomic…

Pictorial matrix elements M_fi in QFT perturbational expansions Calculational Diagram Biophysics & Medical Physics

Fick's Laws of Diffusion

Physical laws describing solute diffusion mass transport across biological concentration gradients.

1st: J = -D (dC / dx); 2nd: ∂C / ∂t = D (∂²C / ∂x²) mol/(m²·s) (Flux J) & m²/s (Diffusion Coefficient D) Plasma Physics

Field-Reversed Configuration (FRC)

A high-beta compact toroid magnetic confinement concept where a closed-poloidal-field plasma torus is sustained inside a simple linear…

Average Beta ⟨β⟩ ≈ 1 (High-Beta Compact Toroid) Dimensionless High Beta ⟨β⟩ ~ 0.9 Quantum & Atomic Physics

Fine Structure

The small splitting of atomic spectral lines resulting from relativistic mass corrections and spin-orbit coupling.

E_fine ~ α² E_n, α ≈ 1 / 137 eV (Energy Splitting) Mathematical & Computational Physics

Finite Difference Method

A numerical method for solving differential equations by approximating derivatives with finite difference quotients on a discretized grid.

f'(x) ≈ (f(x + h) - f(x - h)) / (2 h), f''(x) ≈ (f(x+h) - 2f(x) + f(x-h)) / h² Grid Discretization Method Mathematical & Computational Physics

Finite Element Method (FEM)

A numerical technique for solving complex partial differential equations by subdividing a large physical domain into smaller, simpler…

K u = f (Global Stiffness Matrix Equation) Numerical Mesh Method Quantum & Atomic Physics

Finite Potential Well

A quantum potential well model with barriers of finite energy height V₀.

V(x) = V₀ for |x| > a, V(x) = 0 for |x| ≤ a eV or Joules Thermodynamics & Statistical Physics

First Law of Thermodynamics

A statement of universal energy conservation applied to thermodynamic systems, asserting that internal energy change equals net heat added…

ΔU = Q - W J Quantum & Atomic Physics

Fluorescence

The rapid absorption of light at a shorter wavelength followed by immediate emission of light at a longer wavelength.

h ν_emitted < h ν_absorbed (Stokes Shift) Nanoseconds (Lifetime) Biophysics & Medical Physics

Fluorescence Microscopy

An optical microscopy technique utilizing fluorophores excited by specific light wavelengths to image cellular structures with high…

Abbe Diffraction Limit: d_min = λ / (2 NA) ≈ 200 nm nm (Spatial Resolution) Biophysics & Medical Physics

Fluoroscopy

A dynamic X-ray imaging technique obtaining real-time moving video images of interior anatomical structures and contrast agents.

Real-time continuous low-dose X-ray video acquisition Frames per Second (fps) & Dose Rate (mGy/min) Plasma Physics

Fokker-Planck Equation for Plasmas

The kinetic equation describing the time evolution of a plasma velocity distribution function subject to small-angle Coulomb collisions.

(∂f / ∂t)_coll = -∇_v · (A f) + ½ ∇_v ∇_v : (B f) Kinetic Collision Operator Classical Mechanics

Force

A vector interaction that, when unopposed, alters the state of motion or deforms a physical body.

F = m a = dp/dt N (kg·m/s²) Waves, Oscillations & Acoustics

Forced Oscillations

Oscillations produced in a system subjected to a periodic external driving force.

m (d²x/dt²) + b (dx/dt) + k x = F0 cos(ω t) m Mathematical & Computational Physics

Fourier Series

An expansion of a periodic function f(x) into an infinite sum of orthogonal sine and cosine harmonic functions.

f(x) = a₀/2 + ∑_(n=1)^(∞) [a_n cos(n x) + b_n sin(n x)] Harmonic Series Expansion