NSEP flashcards
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- Coulomb's law
- Force between two point charges in vacuum is F = k|q₁q₂|/r², directed along the line joining them, with k = 9×10⁹ N·m²/C²; attractive for unlike charges, repulsive for like charges.
- Electric field of dipole
- On the axis E = 2kp/r³; on the equatorial line E = kp/r³, opposite in direction to p. Dipole moment p = q(2a) points from negative to positive charge.
- Gauss's law
- Total electric flux through a closed surface equals enclosed charge divided by ε₀. Flux through a closed surface is zero when no net charge lies inside, regardless of external fields.
- Electrostatic potential energy
- Potential energy of two charges is U = kq₁q₂/r; potential V = kq/r for a point charge. Work done by an external agent in moving a charge slowly equals qΔV.
- Capacitor energy density
- Energy stored in a capacitor is U = ½CV² = ½QV = Q²/2C. In a dielectric-filled region the field energy per unit volume is u = ½ε₀κE².
- Drift velocity
- v_d = I/(nAe), typically of order 10⁻⁴ m/s in metals. Current density J = nev_d = σE, and resistivity ρ = m/(ne²τ) where τ is relaxation time.
- Kirchhoff's laws
- Junction rule: algebraic sum of currents at a node is zero (charge conservation). Loop rule: algebraic sum of potential differences around any closed loop is zero (energy conservation).
- Wheatstone bridge balance
- Bridge is balanced when P/Q = R/S, giving zero galvanometer deflection. At balance the bridge behaves as if the galvanometer branch were absent, simplifying resistance calculations.
- Potentiometer EMF comparison
- For two cells, E₁/E₂ = l₁/l₂ where l₁ and l₂ are balancing lengths. The potentiometer draws no current at balance, so it measures true EMF, not terminal voltage.
- Motion in magnetic field
- A charge moving perpendicular to a uniform B follows a circle of radius r = mv/(qB) at frequency f = qB/(2πm); a velocity component parallel to B produces a helical path.
- Biot–Savart law
- dB = (μ₀/4π)(I dl sinθ)/r², with direction given by the right-hand rule. Integrating gives B = μ₀I/(2πr) for a long straight wire.
- Ampere's circuital law
- ∮B·dl = μ₀I_enclosed for steady currents. It yields B = μ₀nI inside a long solenoid and B = μ₀I/(2πr) around a long straight conductor.
- Force between parallel currents
- Two long parallel wires separated by d carry force per unit length F/L = μ₀I₁I₂/(2πd); the force is attractive for currents in the same direction and repulsive for opposite directions.
- Faraday's law of induction
- Induced EMF equals the negative rate of change of magnetic flux: ε = −dΦ/dt, where Φ = BA cosθ. The minus sign expresses Lenz's law opposing the change.
- Self-inductance energy
- An inductor opposes current change with ε = −L dI/dt and stores energy U = ½LI². Inductive reactance X_L = ωL rises with frequency, opposing high-frequency AC.
- Transformer relation
- V_s/V_p = N_s/N_p; a step-up transformer has more secondary turns. An ideal transformer conserves power, so V_sI_s = V_pI_p and current falls as voltage rises.
- RMS current and voltage
- I_rms = I₀/√2 and V_rms = V₀/√2 for sinusoids. AC ammeters and voltmeters read RMS values, and average power is P = V_rms I_rms cosφ.
- Series LCR resonance
- Resonance occurs at ω = 1/√(LC), where X_L = X_C, impedance is minimum (Z = R), current is maximum, and the power factor cosφ = R/Z equals one.
- Mirror formula
- 1/f = 1/v + 1/u with sign convention: distances measured from pole, along incident light positive. Magnification m = −v/u; concave mirror f is negative.
- Lens formula and power
- 1/f = 1/v − 1/u; power P = 1/f in dioptres with f in metres. For thin lenses in contact, 1/F = 1/f₁ + 1/f₂.
- Total internal reflection
- Occurs when light travels from denser to rarer medium at incidence above critical angle θ_c, where sinθ_c = 1/n. No refracted ray exists beyond θ_c; light is fully reflected.
- Young's double slit fringes
- Fringe width β = λD/d where D is slit-screen distance and d slit separation. Bright fringes satisfy path difference nλ; dark fringes satisfy (2n−1)λ/2.
- Single slit diffraction
- First minimum at a sinθ = λ. Central maximum width is twice that of secondary maxima, and intensity falls off rapidly on either side of the central bright fringe.
- Photoelectric equation
- hν = φ₀ + K_max, so stopping potential satisfies eV₀ = hν − φ₀. K_max depends on frequency, not intensity; intensity controls photocurrent magnitude.
- de Broglie wavelength
- λ = h/p = h/(mv). For an electron accelerated through V volts, λ ≈ 12.27/√V Å, so higher accelerating voltage gives shorter wavelength and better resolution.
- Bohr model energies
- E_n = −13.6 Z²/n² eV and r_n = 0.53 n²/Z Å. Photon energy in a transition equals E_upper − E_lower, giving spectral lines in the hydrogen series.
- Radioactive decay law
- N = N₀e^(−λt); activity A = λN; half-life T½ = 0.693/λ and mean life τ = 1/λ. After n half-lives, remaining fraction is (1/2)^n.
- Mass defect and binding energy
- Binding energy = Δm c², where Δm is the difference between constituent nucleon masses and the nucleus mass. BE per nucleon peaks near iron, enabling fission and fusion energy release.
- Nuclear fission and fusion
- Fission splits a heavy nucleus into lighter fragments plus neutrons, releasing energy; fusion combines light nuclei. Both release energy because products have higher binding energy per nucleon.
- Semiconductor diode biasing
- Forward bias (p to positive) reduces the depletion width and allows current above the knee voltage; reverse bias widens the depletion layer and permits only a small leakage current.
- Half-wave rectifier
- A single diode passes one half-cycle of AC input, giving pulsating DC output. Ripple frequency equals the input frequency, unlike a full-wave rectifier which doubles it.
- Logic gates truth rules
- AND outputs 1 only if all inputs are 1; OR outputs 1 if any input is 1; NOT inverts. NAND and NOR are universal gates from which all others can be built.