# Electrical Engineering (Intermediate): Electromagnetism, Oscillations, Waves & Optics

> Intermediate physics spanning electrostatics, direct current circuits, magnetic fields and forces, simple harmonic oscillators, mechanical wave propagation, acoustics, and geometric/wave optics.

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- **Markdown URL:** https://flashcards.world/flashcards/sets/17193947-9333-48df-879e-b0b95e6a35d9.md
- **Level:** intermediate
- **Languages:** en → en
- **Total Cards:** 32

## Flashcards (32 Cards)

| # | Front (Term / Prompt) | Back (Definition / Answer) | Example | Multiple-Choice Options |
| :--- | :--- | :--- | :--- | :--- |
| 1 | What causes acoustic beats and what is the beat frequency formula? | Beats are periodic fluctuations in sound volume caused by the constructive and destructive interference of two sound waves possessing slightly different frequencies (f1 and f2). Beat frequency: f_beat = \|f1 - f2\| The combined wave envelope pulses at f_beat, enabling musicians to tune instruments by listening for the elimination of beats. |  |  |
| 2 | What is optical dispersion and why does a glass triangular prism separate white light into a rainbow spectrum? | Dispersion is the phenomenon where a material's refractive index n depends on light frequency/wavelength: n = n(λ). In standard glass, shorter wavelengths (violet light) experience a higher refractive index than longer wavelengths (red light). Therefore, violet light bends (refracts) at a greater angle than red light, dispersing white light into its spectral colors. |  |  |
| 3 | What is the magnetic force exerted on a straight current-carrying wire of length L in a uniform magnetic field B? | F = I · (L x B) = I · L · B · sin(θ) • I = Electric current (A) • L = Vector along length of wire in current direction (m) • B = Magnetic flux density (Tesla, T) • θ = Angle between wire current vector and magnetic field vector. |  |  |
| 4 | What are the three mathematical expressions for electrical power dissipated in a resistor? | P = I · V = I² · R = V² / R • P = Power dissipated as thermal energy (Watts) • I = Current through the resistor (Amperes) • V = Potential difference across the resistor (Volts) • R = Resistance (Ohms) Derived by substituting Ohm's Law (V = IR) into P = dU/dt = (dq/dt)·V = I·V. |  |  |
| 5 | What is the defining differential equation and general solution for Simple Harmonic Motion (SHM)? | Differential equation: d²x / dt² + ω² · x = 0 General solution: x(t) = A · cos(ω·t + φ) • A = Amplitude of oscillation • ω = Angular frequency (rad/s) • φ = Phase constant Acceleration is directly proportional to displacement and directed toward the equilibrium point: a(t) = -ω² · x(t). |  |  |
| 6 | How do harmonic series differ between an acoustic pipe open at both ends versus open at only one end? | • Open at both ends: Antinodes at both ends; supports all integer harmonics:   fn = n · (v / 2L) (n = 1, 2, 3...) • Open at one end, closed at the other: Antinode at open end, node at closed end; supports only ODD harmonics:   fm = m · (v / 4L) (m = 1, 3, 5...); fundamental λ1 = 4L. |  |  |
| 7 | What is Coulomb's Law and what is the electrostatic constant (k_e)? | Coulomb's Law quantifies the electrostatic force between two stationary point charges q1 and q2 separated by distance r in vacuum: F_e = k_e · (\|q1 · q2\|) / r² where k_e = 1 / (4πε0) ≈ 8.988 x 10⁹ N·m²/C². The force is repulsive for like charges and attractive for opposite charges, directed along the line connecting the charges. |  |  |
| 8 | What are Kirchhoff's Current Law (Junction Rule) and Voltage Law (Loop Rule), and what physical conservation laws do they represent? | • Kirchhoff's Current Law (KCL): The algebraic sum of currents entering any circuit node/junction equals zero (Σ I_in = Σ I_out). Represents Conservation of Electric Charge. • Kirchhoff's Voltage Law (KVL): The algebraic sum of all potential differences (voltages) around any closed circuit loop equals zero (Σ ΔV = 0). Represents Conservation of Energy. |  |  |
| 9 | What is the physical nature of sound waves and what equation determines the speed of sound in a fluid? | Sound waves are mechanical longitudinal pressure and density waves requiring a material medium for propagation. Speed of sound in a fluid: v = sqrt(B / ρ) where B is the bulk modulus (elastic resistance to compression) and ρ is the fluid density. Sound travels faster through stiffer, less compressible media (e.g., steel ~5960 m/s > water ~1480 m/s > air ~343 m/s). |  |  |
| 10 | What does Gauss's Law state, and why is the static electric field inside an empty isolated conductor zero? | Gauss's Law states that the net electric flux through any closed Gaussian surface equals the enclosed charge divided by permittivity: ∮ E · dA = Q_enclosed / ε0 Inside an isolated conductor at electrostatic equilibrium, mobile conduction electrons redistribute to the outer surface until internal repulsive forces cancel; thus Q_enclosed = 0 within any interior Gaussian surface, meaning E = 0 throughout the interior. |  |  |
| 11 | What is capacitance (C) and what is the formula for a parallel-plate capacitor with a dielectric material? | Capacitance is the ratio of charge stored to the electric potential difference: C = Q / V (in Farads: 1 F = 1 C/V). For a parallel-plate capacitor with plate area A, separation d, and dielectric constant κ: C = κ · ε0 · (A / d) Inserting a dielectric (κ > 1) increases capacitance by polarizing and reducing the internal electric field for a given stored charge. |  |  |
| 12 | What is the Thin-Lens Equation and what sign conventions apply to focal length? | (1 / f) = (1 / do) + (1 / di) • f = Focal length • do = Object distance (positive for real objects) • di = Image distance (positive for real images on opposite side; negative for virtual images on same side) Sign convention for f: • Converging (convex) lens: f > 0 (positive) • Diverging (concave) lens: f < 0 (negative) |  |  |
| 13 | How is the electric field (E) defined, and how do field line patterns differ between positive and negative point charges? | The electric field E at a point in space is defined as the electrostatic force experienced per unit positive test charge: E = F_e / q0 (in N/C or V/m). • Positive charge (+q): Field lines radiate radially outward in all directions. • Negative charge (-q): Field lines radiate radially inward toward the charge. Field line density corresponds to electric field magnitude. |  |  |
| 14 | How is total mechanical energy conserved during undamped Simple Harmonic Motion? | Total energy E oscillates continuously between kinetic energy (K) and potential energy (U): E = K + U = (1/2)·m·v(t)² + (1/2)·k·x(t)² = (1/2)·k·A² = (1/2)·m·v_max² At maximum displacement (x = ±A), velocity is zero and energy is purely potential; at equilibrium (x = 0), potential energy is zero and kinetic energy is maximized. |  |  |
| 15 | In Young's Double-Slit experiment, what are the conditions for constructive and destructive interference fringes? | For slit separation d, angle θ, and wavelength λ: • Constructive interference (bright fringes): Path difference d·sin(θ) = m · λ (where m = 0, ±1, ±2...) • Destructive interference (dark fringes): Path difference d·sin(θ) = (m + 1/2) · λ (where m = 0, ±1, ±2...) On a screen at distance L (small angle sin(θ) ≈ y/L), fringe separation is Δy = (λ · L) / d. |  |  |
| 16 | What causes acoustic resonance in a driven harmonic oscillator? | Resonance occurs when the frequency of an external driving periodic force matches the natural frequency (ω0) of the oscillating system. At resonance, energy transfer from the driver into the system reaches a maximum, resulting in dramatically amplified oscillation amplitudes limited only by system damping. |  |  |
| 17 | What is the torque experienced by a planar current loop of area A carrying current I in a uniform magnetic field B? | τ = μ x B = μ · B · sin(θ) where μ = N · I · A · n is the magnetic dipole moment vector (with N turns and unit normal n determined by the right-hand curl rule), and θ is the angle between μ and B. The torque acts to align the loop's magnetic moment with the external magnetic field. |  |  |
| 18 | What is lateral magnification (m) for optical lenses and what do its signs indicate? | m = hi / ho = -di / do • hi = Image height, ho = Object height • di = Image distance, do = Object distance Sign interpretation: • m > 0 (Positive): Upright virtual image • m < 0 (Negative): Inverted real image • \|m\| > 1: Magnified (enlarged) image • \|m\| < 1: Reduced (diminished) image |  |  |
| 19 | What does Ampère's Law state for calculating the magnetic field around a long, straight current-carrying wire? | Ampère's Circuital Law states that the line integral of B around a closed loop equals μ0 times the enclosed current: ∮ B · dl = μ0 · I_enc. For a circular path of radius r centered on a long straight wire carrying current I: B · (2πr) = μ0 · I  ==>  B = (μ0 · I) / (2π · r) where μ0 = 4π x 10⁻⁷ T·m/A is vacuum permeability. |  |  |
| 20 | What is the magnetic force on a charged particle moving through a magnetic field, and why does this force do zero work? | Magnetic force: F_B = q · (v x B) = q · v · B · sin(θ) Direction is given by the Right-Hand Rule (perpendicular to both v and B). Work done is zero because instantaneous magnetic force is always orthogonal to velocity (F_B ⊥ v): dW = F_B · dr = F_B · (v dt) = (F_B · v) dt = 0 Magnetic forces can alter a charged particle's trajectory direction, but cannot change its kinetic energy or speed. |  |  |
| 21 | What are the equivalent resistance formulas for resistors connected in series versus in parallel? | • Series: Resistors share identical current; voltages add: R_eq = R1 + R2 + R3 + ... + Rn • Parallel: Resistors share identical voltage; currents add: 1 / R_eq = (1 / R1) + (1 / R2) + (1 / R3) + ... + (1 / Rn) Parallel equivalent resistance is always smaller than the smallest individual resistor. |  |  |
| 22 | What are the formulas for period (T) and angular frequency (ω) of a mass m on an ideal spring of stiffness k? | • Angular frequency: ω = sqrt(k / m) • Period: T = 2π / ω = 2π · sqrt(m / k) • Frequency: f = 1 / T = (1 / 2π) · sqrt(k / m) The period depends solely on mass and spring stiffness, and is completely independent of oscillation amplitude (isochronism). |  |  |
| 23 | Why are equipotential surfaces always perpendicular to electric field lines? | An equipotential surface is a locus of points where potential V is constant (ΔV = 0). The work done moving a charge along an equipotential is W = -q ∫ E · dl = 0. For the dot product E · dl to equal zero for any displacement dl along the surface, the electric field vector E must be orthogonal (perpendicular) to dl everywhere. |  |  |
| 24 | What is total internal reflection and what is the formula for the critical angle (θ_c)? | Total internal reflection occurs when a light ray traveling in a higher refractive index medium (n1) encounters a boundary with a lower index medium (n2 < n1) at an angle of incidence exceeding the critical angle (θ_inc > θ_c), causing 100% of light to reflect back with zero refraction. Critical angle: sin(θ_c) = n2 / n1  (with n1 > n2) Foundation of optical fiber telecommunications. |  |  |
| 25 | What does Ohm's Law state and how is electrical resistance related to resistivity (ρ)? | Ohm's Law states that current through an ohmic conductor is directly proportional to voltage across it: V = I · R (where R is constant resistance in Ohms, Ω). Resistance of a uniform conductor of length L and cross-sectional area A is: R = ρ · (L / A) where ρ is material resistivity (Ω·m), which depends on atomic structure and temperature. |  |  |
| 26 | What are the harmonic frequencies for standing waves on a stretched string of length L fixed at both ends? | fn = n · (v / 2L) = n · f1 (where n = 1, 2, 3...) • Fundamental frequency (n = 1): f1 = v / 2L (wavelength λ1 = 2L) • v = sqrt(T_tension / μ_linear_density) Nodes exist at both fixed ends, with antinodes in between; all integer harmonics (both odd and even) are present. |  |  |
| 27 | What is the relationship between electric potential energy (U), electric potential (V), and work done moving a charge? | Electric potential V is electric potential energy per unit charge: V = U / q (in Volts: 1 V = 1 J/C). The work done by an external agent moving charge q without acceleration between two points with potential difference ΔV is: W_ext = q · ΔV = q · (V_final - V_initial) Conversely, work done by the conservative electric field is W_field = -q · ΔV. |  |  |
| 28 | What is the period (T) of a simple gravity pendulum of length L under the small-angle approximation? | T = 2π · sqrt(L / g) Derived from restoring torque τ = -m·g·L·sin(θ) ≈ -m·g·L·θ for small angles (sin(θ) ≈ θ in radians). The period is independent of the bob's mass and oscillation amplitude. |  |  |
| 29 | How do equivalent capacitances combine in series versus in parallel? | • Parallel: Capacitors share identical voltage; stored charges add: C_eq = C1 + C2 + C3 + ... + Cn • Series: Capacitors share identical stored charge; voltages add: 1 / C_eq = (1 / C1) + (1 / C2) + (1 / C3) + ... + (1 / Cn) (Notice this is the inverse of the resistor combination rules). |  |  |
| 30 | How is sound intensity level (β) measured in decibels (dB)? | β = 10 · log10(I / I0) • I = Acoustic sound intensity (W/m²) • I0 = Reference threshold of human hearing at 1000 Hz (1.0 x 10⁻¹² W/m²) Because the decibel scale is logarithmic, an increase of 10 dB represents a 10-fold increase in sound intensity, and an increase of 20 dB represents a 100-fold increase. |  |  |
| 31 | What are the Law of Reflection and Snell's Law of Refraction? | • Law of Reflection: Angle of incidence equals angle of reflection (θ_inc = θ_refl), measured relative to the surface normal. • Snell's Law of Refraction: n1 · sin(θ1) = n2 · sin(θ2) where n1 and n2 are refractive indices of the two media. When light enters an optically denser medium (n2 > n1), it slows down and bends toward the normal (θ2 < θ1). |  |  |
| 32 | What is Malus's Law for linearly polarized light passing through an optical polarizer? | I = I0 · cos²(θ) • I0 = Initial intensity of linearly polarized light entering the analyzer • I = Transmitted light intensity exiting the analyzer • θ = Angle between the transmission axis of the incident polarized light and the analyzer axis If θ = 90° (crossed polarizers), transmitted intensity drops to zero. |  |  |

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