Physics Part I

NCERT Class 12 Physics Chapter 1 covers Electric Charges and Fields, explaining how electric charges arise, Coulomb's law for forces between point charges, the concept of electric field and field lines, electric flux, Gauss's law, and electric dipoles — forming the foundation of electrostatics.

• 1Electric charges are of two types — positive and negative; like charges repel and unlike charges attract each other.
• 2Charge is conserved (cannot be created or destroyed), additive (charges sum algebraically), and quantised: q = ne where e = 1.602 × 10⁻¹⁹ C.
• 3Coulomb's law: the electrostatic force between two point charges q₁ and q₂ separated by distance r in vacuum is F = (1/4πε₀)(q₁q₂/r²), where ε₀ = 8.854 × 10⁻¹² C² N⁻¹ m⁻².
• 4The electric field E at a point is the force per unit positive test charge placed there; for a point charge Q, E = (1/4πε₀)(Q/r²). Field lines start on positive charges and end on negative charges and never cross.
• 5Gauss's law states that the total electric flux through any closed surface equals q/ε₀, where q is the total charge enclosed — a powerful tool for symmetric charge distributions.

Chapter 2 of NCERT Class 12 Physics Part I covers electrostatic potential and capacitance, explaining how electric potential is the work done per unit positive charge in bringing it from infinity to a point, and how capacitors store energy using the relation C = Q/V.

• 1Electrostatic potential at a point equals the work done by an external force per unit positive charge in bringing it from infinity to that point, with potential at infinity taken as zero.
• 2Potential due to a point charge Q at distance r is V = Q/(4πε₀r); for a dipole it falls off as 1/r² and depends on the angle with the dipole moment.
• 3Equipotential surfaces are always perpendicular to the electric field; no work is done moving a charge along an equipotential surface.
• 4Inside a conductor the electric field is zero, potential is constant throughout, and any excess charge resides only on the outer surface (electrostatic shielding applies to cavities).
• 5Capacitance C = Q/V depends only on geometry; for a parallel plate capacitor C = ε₀A/d, and inserting a dielectric of constant K increases it to C = Kε₀A/d.

NCERT Class 12 Physics Chapter 3, Current Electricity, covers the flow of electric charges through conductors, Ohm's law (V = RI), resistivity, drift velocity of electrons, Kirchhoff's rules, and circuit analysis tools such as the Wheatstone bridge.

• 1Electric current is defined as the net charge flowing per unit time across a cross-section: I = Q/t (steady) or I = lim(ΔQ/Δt) as Δt→0 (instantaneous).
• 2Ohm's law states V = RI, where resistance R = ρl/A; resistivity ρ depends on material and temperature but not on the conductor's dimensions.
• 3Drift velocity of electrons under an electric field E is vd = –eEτ/m, where τ is the relaxation (average collision) time, giving conductivity σ = ne²τ/m.
• 4Resistivity of metals increases with temperature (ρT = ρ0[1 + α(T – T0)]), while resistivity of semiconductors decreases with increasing temperature.
• 5For a cell of EMF ε and internal resistance r connected to external resistance R, current I = ε/(R + r) and terminal voltage V = ε – Ir.

Chapter 4 of Class 12 Physics Part I covers Moving Charges and Magnetism, explaining how electric currents and moving charges produce magnetic fields and how magnetic fields exert forces on moving charges and current-carrying conductors, governed by laws including the Lorentz force, Biot-Savart law, and Ampere's Circuital Law.

• 1The Lorentz force on a charge q moving with velocity v in magnetic field B is F = q(v × B), always perpendicular to v, so the magnetic force does no work on the particle.
• 2A charged particle moving perpendicular to a uniform magnetic field follows a circular path of radius r = mv/qB; the cyclotron frequency ν = qB/2πm is independent of the particle's speed.
• 3The Biot-Savart law states dB = (μ₀/4π)(I dl × r̂)/r², giving the magnetic field contribution from an infinitesimal current element; the field at the centre of a circular loop of radius R is B = μ₀I/2R.
• 4Ampere's Circuital Law (∮B·dl = μ₀I) gives the field outside a long straight wire as B = μ₀I/2πR and inside a long solenoid as B = μ₀nI, where n is turns per unit length.
• 5Parallel currents attract each other and anti-parallel currents repel; this interaction defines the SI unit of current — the ampere.

NCERT Class 12 Physics Chapter 5, Magnetism and Matter, covers the properties of bar magnets, Gauss's law for magnetism, magnetisation, magnetic intensity, and the classification of materials as diamagnetic, paramagnetic, or ferromagnetic.

• 1A bar magnet acts as a magnetic dipole; its axial field is B = μ₀·2m / (4πr³) and equatorial field is B = –μ₀m / (4πr³) for r >> l.
• 2Gauss's law for magnetism states the net magnetic flux through any closed surface is zero (∮ B·dS = 0), because isolated magnetic monopoles do not exist.
• 3Magnetisation M is the net magnetic moment per unit volume; the total field in a material is B = μ₀(H + M), where H is the magnetic intensity.
• 4Magnetic susceptibility χ relates M and H by M = χH; relative permeability μr = 1 + χ and permeability μ = μ₀μr.
• 5Diamagnetic materials (e.g., bismuth, copper, water) are repelled by magnets (χ < 0); paramagnetic materials (e.g., aluminium, oxygen) are weakly attracted (χ small and positive).

Electromagnetic induction is the phenomenon in which a changing magnetic field induces an electric current in a closed coil, discovered around 1830 by Michael Faraday in England and Joseph Henry in the USA, and described by Faraday's law: ε = −N(dΦB/dt).

• 1Electromagnetic induction: electric current is induced in a coil whenever the magnetic flux through it changes with time (Faraday, Henry, ~1830).
• 2Faraday's law: induced emf ε = −N(dΦB/dt); for a single-turn circuit, ε = −dΦB/dt, where magnetic flux ΦB = BA cos θ (SI unit: weber, Wb).
• 3Lenz's law: the induced current flows in a direction that opposes the change in magnetic flux producing it, consistent with conservation of energy.
• 4Motional emf: a conductor of length l moving with velocity v perpendicular to a uniform field B develops emf ε = Blv across its ends.
• 5Self-inductance L of a solenoid: L = μr μ0 n² Al; self-induced emf ε = −L(dI/dt); energy stored W = ½LI²; mutual inductance M satisfies ε1 = −M(dI2/dt).

Alternating Current (AC) is a current whose magnitude and direction vary sinusoidally with time; it is the dominant form of electrical power because AC voltages can be efficiently stepped up or down using transformers, enabling economical long-distance transmission.

• 1In a pure resistor, voltage and current are in phase; rms current I = im/√2 = 0.707 im and rms voltage V = vm/√2 = 0.707 vm.
• 2In a pure inductor, current lags voltage by π/2; inductive reactance XL = ωL (unit: ohm); average power over a full cycle is zero.
• 3In a pure capacitor, current leads voltage by π/2; capacitive reactance XC = 1/ωC (unit: ohm); average power over a full cycle is zero.
• 4In a series LCR circuit, impedance Z = √[R² + (XC − XL)²] and resonance occurs at ω₀ = 1/√LC, where current amplitude is maximum (im = vm/R).
• 5Average power in an AC circuit is P = VI cos φ, where cos φ is the power factor; in purely inductive or capacitive circuits cos φ = 0, giving zero net power (wattless current).

Electromagnetic waves are coupled oscillating electric and magnetic fields that propagate through space at the speed of light (3×10⁸ m/s) in vacuum, arising from Maxwell's equations and produced by accelerated charges.

• 1Maxwell introduced displacement current (id = ε₀ dΦE/dt) to fix an inconsistency in Ampere's circuital law when applied to a charging capacitor.
• 2Accelerated (not stationary or uniformly moving) charges produce electromagnetic waves; the wave frequency equals the frequency of charge oscillation.
• 3In an electromagnetic wave, E and B are perpendicular to each other and to the direction of propagation, related by E₀/B₀ = c.
• 4The speed of EM waves in vacuum is c = 1/√(μ₀ε₀) ≈ 3×10⁸ m/s; in a medium it becomes v = 1/√(με).
• 5Hertz first experimentally demonstrated electromagnetic waves in 1887; Jagdish Chandra Bose later produced shorter-wavelength EM waves (25 mm to 5 mm).