Class 12 Physics Complete Notes — Electrostatics, Magnetism, Optics, Modern Physics

Unit 1: Electrostatics

Coulomb's Law

Force between two charges: F = kq₁q₂/r²

• k = 9×10⁹ N·m²/C²
• ε₀ = 8.85×10⁻¹² C²/(N·m²)
• k = 1/(4πε₀)

Electric Field: E = F/q = kQ/r² (N/C or V/m)

Electric Field Lines:

• Start from positive, end at negative charge
• Never intersect
• Tangent gives direction of E at that point
• Density indicates field strength

Gauss's Law

Φ = Q_enc/ε₀

Applications:

• Spherical shell: E = kQ/r² outside; E = 0 inside
• Infinite line charge: E = λ/(2πε₀r)
• Infinite plane: E = σ/(2ε₀)

Electric Potential

V = kQ/r (potential at distance r from charge Q)

• Potential energy: U = kq₁q₂/r
• Relation: E = -dV/dr
• Work done: W = q(V_A - V_B) = q·V

Equipotential surfaces: No work done moving charge along them; perpendicular to E field lines.

Capacitors

Capacitance: C = Q/V = ε₀A/d (parallel plate)

Energy stored: U = ½CV² = Q²/(2C) = ½QV

Combination:

• Series: 1/C = 1/C₁ + 1/C₂
• Parallel: C = C₁ + C₂

Dielectric: Inserting dielectric (constant K): C → KC, E → E/K, V → V/K

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Unit 2: Current Electricity

Current: I = dQ/dt = nAve (n=electron density, A=area, v=drift velocity)

Ohm's Law: V = IR; Resistivity ρ = RA/L

Temperature effect: R_T = R₀(1 + αT)

EMF and Internal Resistance:

• Terminal voltage = EMF − Ir
• V = ε − Ir (discharging); V = ε + Ir (charging)

Kirchhoff's Laws:

• KCL (Junction Rule): Sum of currents at junction = 0 (charge conservation)
• KVL (Loop Rule): Sum of EMFs and voltage drops in closed loop = 0 (energy conservation)

Wheatstone Bridge: P/Q = R/S (balanced bridge — no current through galvanometer)

Potentiometer: Used to measure EMF without drawing current — more accurate than voltmeter.

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Unit 3: Magnetism

Biot-Savart Law: dB = (μ₀/4π)(I dl × r̂)/r²

Ampere's Law: ∮B·dl = μ₀I_enc

Magnetic force on moving charge: F = q(v × B) = qvB sin θ

Lorentz Force: F = qE + q(v × B)

Torque on current loop: τ = NIA × B = MB sin θ (M = NIA = magnetic moment)

Cyclotron: Charged particle in magnetic field moves in circle; r = mv/(qB); T = 2πm/(qB) — independent of velocity!

Electromagnetic Induction

Faraday's Law: EMF = -dΦ/dt

Lenz's Law: Induced current opposes change causing it (negative sign in Faraday)

Motional EMF: ε = Blv (conductor of length l moving with velocity v in field B)

Self-Inductance: V = -L(dI/dt); Energy in inductor = ½LI²

Mutual Inductance: e₂ = -M(dI₁/dt)

Transformer: V₁/V₂ = N₁/N₂; I₁/I₂ = N₂/N₁

• Step-up: N₂ > N₁; Step-down: N₂ < N₁
• Efficiency = (Output power/Input power) × 100

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Unit 4: Wave Optics

Huygens' Principle: Every point on a wavefront acts as secondary source of waves.

Young's Double Slit Experiment (YDSE):

• Fringe width: β = λD/d
• Condition for bright fringes: path difference = nλ
• Condition for dark fringes: path difference = (2n-1)λ/2

Diffraction: Bending of light around obstacles

• Single slit: first minimum at sin θ = λ/a

Polarization: Transverse nature of light

• Malus's Law: I = I₀cos²θ (after polarizer at angle θ)
• Brewster's Law: tan θ_B = n (polarization angle)

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Unit 5: Modern Physics

Photoelectric Effect

• Threshold frequency (ν₀): Minimum frequency for electron emission
• Einstein's equation: KE_max = hν - φ (φ = work function = hν₀)
• Stopping potential: eV₀ = KE_max
• Key: frequency determines emission; intensity determines count of electrons

de Broglie Hypothesis

Every particle has wave nature: λ = h/mv = h/p

Bohr's Model of Hydrogen Atom

• Electrons in fixed circular orbits (stationary states)
• Energy of nth orbit: E_n = -13.6/n² eV
• Radius of nth orbit: r_n = 0.529n² Å (Bohr radius a₀ = 0.529 Å)
• Photon emitted: hν = E_initial - E_final

Spectral Series: | Series | n_f | Region | |---|---|---| | Lyman | 1 | Ultraviolet | | Balmer | 2 | Visible | | Paschen | 3 | Infrared |

Nuclear Physics

Binding Energy: BE = [Zm_p + (A-Z)m_n - M]c²

Radioactive Decay:

• α decay: A/Z → (A-4)/(Z-2) + ⁴₂He
• β⁻ decay: neutron → proton + electron + antineutrino
• γ decay: energy release only, no change in A or Z

Half Life: T₁/₂ = 0.693/λ Decay Law: N = N₀e^(-λt)

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Solved PYQ Questions

Q1 (2023): A charge +2μC is placed at origin. Find potential at 3m. V = kQ/r = (9×10⁹ × 2×10⁻⁶)/3 = 6000 V = 6 kV

Q2 (2023): Find energy stored in 5μF capacitor charged to 100V. U = ½CV² = ½ × 5×10⁻⁶ × 100² = 0.025 J = 25 mJ

Q3 (2022): Find de Broglie wavelength of electron moving at 10⁶ m/s. λ = h/mv = 6.63×10⁻³⁴ / (9.1×10⁻³¹ × 10⁶) λ = 7.28×10⁻¹⁰ m = 0.728 nm

Q4 (2022): Hydrogen atom transitions from n=4 to n=2. Find photon energy. E₄ = -13.6/16 = -0.85 eV E₂ = -13.6/4 = -3.4 eV ΔE = 3.4 - 0.85 = 2.55 eV (Balmer series — visible light)

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Quick Revision Checklist

• Coulomb's Law: F = kq₁q₂/r²; k = 9×10⁹
• Gauss's Law: Φ = Q/ε₀; E=0 inside conductor
• Capacitor energy: U = ½CV²; C_parallel = C1+C2
• Kirchhoff's laws: KCL (junction), KVL (loop)
• Faraday's law: EMF = -dΦ/dt; Lenz's law opposes change
• Transformer: V₁/V₂ = N₁/N₂
• Photoelectric effect: KE = hν - φ; frequency matters, not intensity
• Bohr's model: E_n = -13.6/n² eV; r_n = 0.529n² Å
• de Broglie: λ = h/mv
• Radioactive decay law: N = N₀e^(-λt); T₁/₂ = 0.693/λ