PSEB SS Physics cheat sheet

Coulomb's law: F = (1/4πε0)|q1q2|/r² = k|q1q2|/r², with k ≈ 9×10^9 N m² C⁻²; force is along the line joining point charges.

Electric field E = F/q0; for a point charge E = kQ/r²; field lines begin on positive charge, end on negative charge, and never cross.

Gauss's law: ∮E·dA = q_enclosed/ε0; spherical, cylindrical, or planar symmetry lets E be taken outside the flux integral.

Potential V = W/q; for a point charge V = kQ/r; E = −dV/dr; equipotential surfaces are perpendicular to electric field lines.

Capacitance C = Q/V; parallel plates C = ε0A/d, multiplied by dielectric constant κ when fully filled; series 1/C = Σ1/Ci, parallel C = ΣCi.

Energy stored U = ½CV² = ½QV = Q²/(2C); electric energy density in vacuum is ½ε0E².

Static conductor: E = 0 inside; net charge resides on outer surface; field just outside is σ/ε0 normal to surface; charge density is higher at sharp points.

Dipole moment p = q(2a); torque τ = p×E; potential energy U = −p·E; axial field E = 2kp/r³ and equatorial field E = kp/r³ for a short dipole.

Electric current I = dQ/dt; for a uniform conductor, current density J = I/A = nev_d, where n is carrier number density and v_d is drift velocity.

Ohm's law V = IR for a metallic conductor at constant temperature; resistance R = ρL/A and resistivity ρ = m/(ne²τ).

Metals: resistivity rises with temperature because lattice scattering increases; semiconductors: resistivity falls with temperature as carrier density rises.

Series: R = ΣRi and same current; parallel: 1/R = Σ1/Ri and same voltage.

EMF ε and internal resistance r give terminal voltage V = ε − Ir; power delivered to external R is I²R.

Kirchhoff's rules: junction ΣI = 0; loop ΣΔV = 0; Wheatstone bridge balance when R1/R2 = R3/R4.

Metre bridge: unknown R/S = l/(100 − l), with l in cm from the end connected to R; potentiometer compares emfs using balancing lengths.

Heating power H/t = I²R = V²/R; maximum power transfer to a load occurs when external R equals internal r.

Moving charge: F = q(v×B), magnitude qvB sinθ; direction from right-hand rule; magnetic force is perpendicular to velocity and does zero work.

Biot–Savart: dB = (μ0/4π) I dl×r/r³; long straight wire B = μ0I/(2πr); circular loop centre B = μ0I/(2R); solenoid B = μ0nI.

Ampere's law: ∮B·dl = μ0I_enclosed; use symmetry for long wire, solenoid, toroid; field inside ideal solenoid is uniform.

Force on current wire F = I L×B; parallel wires: F/L = μ0I1I2/(2πd), currents in same direction attract, opposite directions repel.

Current loop: magnetic moment m = NIA; torque τ = m×B; potential energy U = −m·B; moving-coil galvanometer deflection proportional to current.

Galvanometer conversion: ammeter shunt S = IgG/(I − Ig); voltmeter series resistance R = V/Ig − G.

Magnetic materials: diamagnetic weakly repelled; paramagnetic weakly attracted and temperature-dependent; ferromagnetic domains give strong attraction and hysteresis.

Earth's magnetic elements: declination angle between geographic and magnetic meridians; dip angle of field with horizontal; horizontal component BH = B cosδ.

Faraday's law: ε = −dΦ/dt; Lenz's law says induced current opposes the flux change; motional emf for a rod is ε = Blv.

Self-inductance: ε = −L dI/dt; long solenoid L = μ0n²Al; energy stored in inductor U = ½LI².

Mutual inductance: ε2 = −M dI1/dt; ideal transformer Vs/Vp = Ns/Np = Ip/Is, with power conserved.

AC quantities: rms current I_rms = I0/√2 and V_rms = V0/√2; mean current over a full cycle is zero.

Series LCR: X_L = ωL, X_C = 1/(ωC), Z = √(R² + (X_L − X_C)²), tanφ = (X_L − X_C)/R.

Resonance: X_L = X_C, ω0 = 1/√(LC), Z = R, current maximum, power factor cosφ = 1.

AC power: P = V_rms I_rms cosφ; purely inductive or capacitive load has φ = 90° and zero average power.

Transformer losses: copper I²R heating, eddy currents reduced by lamination, hysteresis reduced by soft iron core, flux leakage reduced by close winding.

An accelerating charge radiates electromagnetic waves; E and B are perpendicular to each other and to propagation, and both oscillate in phase.

In vacuum c = 1/√(μ0ε0) ≈ 3×10^8 m/s; E0/B0 = c; in a medium v = 1/√(με) and refractive index n = c/v.

Spectrum increasing wavelength: gamma rays, X-rays, ultraviolet, visible, infrared, microwaves, radio waves; frequency order is opposite.

Energy density: u = ½ε0E² + B²/(2μ0); average intensity I = ½ε0E0²c; momentum carried is U/c.

Displacement current I_d = ε0 dΦE/dt; it completes the Ampere–Maxwell law across a charging capacitor.

Visible light spans about 400–700 nm, corresponding to frequencies about 4.3×10^14 to 7.5×10^14 Hz.

Radiation pressure: I/c for complete absorption; about 2I/c for normal perfect reflection; solar sails use this momentum transfer.

EM waves need no medium, travel through vacuum, and show reflection, refraction, interference, diffraction, and polarization.

Mirror formula 1/f = 1/v + 1/u with sign convention; lens formula 1/f = 1/v − 1/u; f = R/2 for a spherical mirror.

Refraction: n1 sin i = n2 sin r; n = c/v; critical angle sin C = n2/n1 for n1 > n2; total internal reflection occurs beyond C.

Lens maker: 1/f = (n − 1)(1/R1 − 1/R2); power P = 1/f in dioptres when f is in metres; converging lens has positive power.

Optical instruments: simple microscope M = 1 + D/f; compound microscope M ≈ (v0/u0)(D/fe); telescope M = f0/fe and length f0 + fe.

Young's double slit: path difference d sinθ; bright fringes d sinθ = nλ; dark fringes d sinθ = (2n − 1)λ/2; fringe width β = λD/d.

Single-slit diffraction: minima at a sinθ = nλ; central maximum angular half-width ≈ λ/a; narrower slit gives wider diffraction pattern.

Polarization: Malus law I = I0 cos²θ; Brewster angle tan i_p = n2/n1; reflected light is partially or fully polarized at Brewster incidence.

Huygens principle: every point on a wavefront acts as a secondary wavelet source; the envelope gives the new wavefront and explains reflection and refraction.

Photon energy E = hν = hc/λ; h = 6.63×10^-34 J s; useful relation E(eV) ≈ 1240/λ(nm).

Photoelectric effect: hν = φ + Kmax; threshold frequency ν0 = φ/h; stopping potential eV0 = Kmax.

Intensity controls number of photoelectrons per second; frequency controls maximum kinetic energy, provided ν > ν0.

de Broglie wavelength λ = h/p = h/√(2mK); electron accelerated through V volts has λ ≈ 12.27/√V Å.

Photon momentum p = E/c = h/λ; radiation pressure follows from this momentum transfer.

Davisson–Germer experiment diffracted electrons from a crystal, confirming matter waves; diffraction pattern depends on λ.

Work function is minimum energy needed to remove an electron from a metal surface; alkali metals have low work functions and visible thresholds.

Photoelectric current increases with intensity and saturates when all emitted electrons reach the anode.

Rutherford scattering showed a small massive positive nucleus; nuclear radius about 10^-15 m versus atomic radius about 10^-10 m.

Bohr quantisation: mvr = nh/(2π); hydrogen-like radii rn = 0.529 n²/Z Å; energies En = −13.6 Z²/n² eV.

Hydrogen spectral series: 1/λ = R(1/n1² − 1/n2²); Lyman n1=1 (UV), Balmer n1=2 (visible), Paschen n1=3 (IR).

Nucleus notation A_Z X; mass defect Δm = [Z mp + (A−Z) mn] − M_nucleus; binding energy BE = Δm c²; 1 u = 931.5 MeV.

Radioactive decay: N = N0 e^(−λt) = N0(1/2)^(t/T); activity A = λN; half-life T = ln2/λ; mean life τ = 1/λ.

Alpha decay reduces A by 4 and Z by 2; beta-minus increases Z by 1 with A unchanged and emits an antineutrino; gamma changes neither A nor Z.

Fission of heavy nuclei releases energy because fragments have higher binding energy per nucleon; fusion of light nuclei powers stars.

Nuclear conservation: charge Z, mass number A, momentum, and total energy are conserved in nuclear reactions.

Intrinsic semiconductor: n_e = n_h = n_i; conductivity σ = e(n_e μ_e + n_h μ_h); heating increases n_i and conductivity.

Doping: pentavalent donor gives n-type with electrons majority; trivalent acceptor gives p-type with holes majority; crystal remains electrically neutral.

p-n junction: depletion region has immobile ions and a barrier potential; forward bias reduces barrier and widens current; reverse bias raises barrier.

Diode I–V: significant current above forward threshold; reverse saturation current small until breakdown; Zener breakdown gives regulated reverse voltage.

Rectifiers: half-wave uses one diode; full-wave centre-tap uses two; bridge uses four; output is pulsating DC, filtered by a capacitor.

Transistor: emitter-base forward biased, collector-base reverse biased in active mode; β = IC/IB; α = IC/IE; β = α/(1 − α).

Logic gates: AND outputs 1 only for all 1 inputs; OR for any 1; NOT inverts; NAND and NOR are universal gates.

Energy bands: conductors have overlapping bands; semiconductors have small gap (~1 eV); insulators have large gap; LEDs and photodiodes use direct gap transitions.