Tamil Nadu HSE Second Year Physics cheat sheet

Coulomb force between two point charges: F = (1/4πε0) q1q2/r²; in a medium replace ε0 by ε = εrε0; the force acts along the line joining the charges.

Electric field E = F/q0; for a point charge E = (1/4πε0) Q/r²; field lines start on positive charge and end on negative charge and never cross.

Electric potential V = W/q; point charge V = (1/4πε0) Q/r; E = -dV/dr; equipotential surfaces are perpendicular to field lines.

Gauss law: ∮E·dA = q_enclosed/ε0; inside a conductor in electrostatic equilibrium E = 0 and excess charge resides on the surface.

Capacitance C = Q/V; parallel-plate capacitor C = ε0A/d, multiplied by εr when the space is filled with a dielectric.

Capacitor combinations: series 1/C = 1/C1 + 1/C2 + ...; parallel C = C1 + C2 + ...; series has same charge, parallel same voltage.

Energy stored in a capacitor U = ½CV² = Q²/(2C) = ½QV; energy density in electric field u = ½ε0E².

Electric dipole moment p = q(2a) from negative to positive; torque τ = p × E; potential energy U = -p·E; axial field 2kp/r³ and equatorial field kp/r³ for a short dipole.

Current I = dQ/dt; drift relation I = nAevd; current density J = I/A = nevd, where vd is drift velocity.

Ohm's law V = IR for an ohmic conductor at constant temperature; resistivity ρ = RA/L and resistance R = ρL/A.

Series resistances add: R = R1 + R2 + ...; parallel resistances satisfy 1/R = 1/R1 + 1/R2 + ...; series current is same, parallel voltage is same.

Temperature dependence R = R0(1 + αΔT); metals have positive α, semiconductors negative α; a superconductor has zero resistance below Tc.

Terminal voltage of a cell: V = ε - Ir during discharge and V = ε + Ir during charging, where r is internal resistance.

Kirchhoff rules: junction ΣI = 0; closed loop Σε = ΣIR, with emf positive when traversed from negative to positive terminal.

Wheatstone bridge balance condition R1/R2 = R3/R4; at balance the galvanometer current is zero; a potentiometer also uses a null method and draws no current at balance.

Electric power P = VI = I²R = V²/R; commercial energy is measured in kWh; a fuse is rated for the maximum safe current.

Cells in series: ε = ε1 + ε2 + ... and r = r1 + r2 + ...; identical cells in parallel have ε same and r/n; maximum power transfer to load when R = r.

Magnetic force on a moving charge F = qv × B; magnitude F = qvB sinθ; force is perpendicular to both velocity and magnetic field.

Charge moving perpendicular to uniform B follows a circle: r = mv/(qB); period T = 2πm/(qB) is independent of speed; helical path occurs if v has a component along B.

Biot-Savart law dB = (μ0/4π) I dl sinθ/r²; straight wire B = μ0I/(2πr); circular loop centre B = μ0I/(2R); long solenoid B = μ0nI.

Ampere circuital law ∮B·dl = μ0I_enclosed; useful for straight conductors, solenoids and toroids with suitable symmetry.

Force per unit length between parallel wires F/L = μ0I1I2/(2πd); currents in the same direction attract, opposite directions repel.

Torque on a current loop τ = NIAB sinθ; magnetic dipole moment m = NIA; potential energy U = -m·B.

Moving-coil galvanometer deflection I = kθ; conversion to ammeter uses a low shunt resistance in parallel; conversion to voltmeter uses a high resistance in series.

Earth's magnetic elements: declination D, dip δ and horizontal component BH; tanδ = BV/BH and total field B = √(BH² + BV²).

Faraday law ε = -dΦ/dt; Lenz law gives the minus sign and states that induced current opposes the change in magnetic flux.

Motional emf for a straight conductor moving perpendicular to B: ε = Blv; direction follows Fleming's right-hand rule or Lenz law.

Self-induced emf ε = -L dI/dt; long solenoid L = μ0N²A/l; magnetic energy stored U = ½LI².

Mutual induction ε2 = -M dI1/dt; mutual inductance depends on coil geometry, turns and core permeability; it is the basis of the transformer.

AC quantities: rms current Irms = I0/√2 and rms voltage Vrms = V0/√2; average current over one full cycle is zero.

Reactance X_L = ωL and X_C = 1/(ωC); series LCR impedance Z = √(R² + (X_L - X_C)²) and tanφ = (X_L - X_C)/R.

Series resonance occurs at ω0 = 1/√(LC); at resonance Z = R is minimum, current is maximum, and Q factor = ω0L/R = 1/(ω0CR).

Ideal transformer Vs/Vp = Ns/Np and VpIp = VsIs; step-up raises voltage and lowers current; laminations reduce eddy-current loss.

AC generator emf ε = NBAω sinωt; split-ring commutator gives DC output; average AC power P = VrmsIrms cosφ and wattless current flows when φ = 90°.

Spherical mirror formula 1/f = 1/v + 1/u with f = R/2; magnification m = -v/u; use Cartesian sign convention consistently.

Refraction: n1 sin i = n2 sin r; refractive index n = c/v; critical angle for denser-to-rarer medium sin C = 1/n.

Thin lens formula 1/f = 1/v - 1/u and magnification m = v/u; power P = 1/f in dioptres with f in metres.

Prism relation A + δ = i + e; at minimum deviation n = sin[(A + Dm)/2]/sin(A/2); dispersion separates colours because n varies with wavelength.

Young double-slit fringe width β = λD/d; bright fringes have path difference nλ; dark fringes have path difference (2n - 1)λ/2.

Diffraction grating maxima: (a + b) sinθ = nλ; narrower slits and larger slit spacing produce sharper, more widely spaced principal maxima.

Polarization: Malus law I = I0 cos²θ; Brewster angle tan ip = n; polarization confirms the transverse nature of light.

Optical instruments: simple microscope M = 1 + D/f; telescope magnifying power M = fo/fe; myopia is corrected by a concave lens and hypermetropia by a convex lens.

Photon energy E = hν = hc/λ; photon momentum p = h/λ; h = 6.626 × 10⁻³⁴ J s.

Photoelectric equation Kmax = hν - W = hν - hν0; stopping potential satisfies eV0 = Kmax.

No photoelectrons are emitted below threshold frequency ν0 regardless of intensity; above ν0, saturation current depends on intensity and Kmax depends on frequency.

de Broglie wavelength λ = h/p = h/(mv) = h/√(2mK); for an electron accelerated through V volts, λ ≈ 1.227/√V nm.

Davisson-Germer electron diffraction confirmed matter waves; discrete diffraction maxima match the de Broglie wavelength.

X-ray continuous spectrum has minimum wavelength λmin = hc/(eV); characteristic X-rays arise from inner-shell electron transitions.

Compton effect Δλ = (h/mec)(1 - cosθ); the shift confirms photon momentum and particle-like behaviour of radiation.

Bohr atom: mvr = nh/2π; En = -13.6 Z²/n² eV; rn = 0.529 n²/Z Å; spectral line energy hν = E2 - E1.

Rydberg formula 1/λ = R(1/n1² - 1/n2²); Lyman series is ultraviolet, Balmer visible, Paschen and higher series infrared for hydrogen.

Mass defect Δm = Zmp + (A - Z)mn - M; binding energy BE = Δmc²; BE per nucleon is maximum near iron-56.

Radioactive decay N = N0e^(-λt); half-life T1/2 = 0.693/λ; activity A = λN also decreases with the same half-life.

Alpha decay reduces Z by 2 and A by 4; beta-minus emission increases Z by 1; gamma emission changes neither Z nor A.

Nuclear fission splits a heavy nucleus and releases energy and neutrons; fusion joins light nuclei and powers the Sun; both conserve Z, A and total energy.

Nuclear reactor parts: fuel rods supply fissile material, moderator slows neutrons, control rods absorb neutrons, and shielding absorbs radiation.

Intrinsic semiconductor has equal electron and hole concentrations; conductivity σ = e(neμe + nhμh); conductivity increases with temperature.

n-type doping uses pentavalent donors and makes electrons majority carriers; p-type doping uses trivalent acceptors and makes holes majority carriers.

PN junction has a depletion region and barrier potential; forward bias reduces the barrier and allows majority-carrier current; reverse bias widens the barrier.

Half-wave rectifier uses one diode and gives pulsating DC; full-wave rectifier uses two diodes with centre-tap or four diodes in a bridge.

Zener diode operates in reverse breakdown and is used as a voltage regulator; photodiode, LED and solar cell are optoelectronic devices.

Transistor relations α = IC/IE, β = IC/IB and β = α/(1 - α); CE configuration gives voltage and current gain and phase reversal.

Transistor regions: cutoff when both junctions are reverse biased, active when emitter-base forward and collector-base reverse, saturation when both forward biased.

Logic gates: OR gives high if any input is high; AND gives high only if all inputs are high; NOT inverts; NAND and NOR are universal gates.

Communication system has transmitter, channel and receiver; baseband signals are transmitted directly, while passband systems shift them to a carrier frequency.

Modulation varies a carrier parameter with the message signal; it enables efficient antenna radiation, multiplexing and reduced interference between stations.

AM varies carrier amplitude; modulation index m = Am/Ac; sidebands are fc ± fm and bandwidth is 2fm.

FM varies carrier frequency; bandwidth is approximately 2(Δf + fm); FM has better noise immunity than AM but needs greater bandwidth.

Antenna height should be about λ/4 for efficient radiation; ground-wave propagation suits low frequencies, sky wave uses ionospheric reflection, space wave is line-of-sight.

Satellite communication uses microwaves through a transponder; optical fibre communication uses total internal reflection and has low attenuation and high bandwidth.

Digital modulation includes ASK, FSK and PSK; PCM samples the signal, quantizes it and encodes it in binary.

Demodulation recovers the baseband signal at the receiver; repeaters regenerate or amplify signals to extend communication distance.