⚛️ JEE Physics

1 Physics and Measurement

Every physical quantity is expressed in terms of 7 SI base units (metre, kilogram, second, ampere, kelvin, mole, candela). Dimensional analysis checks whether an equation is physically consistent — both sides must have the same dimensional formula — and can also be used to derive the form of a relation between quantities.

Significant figures: all non-zero digits are significant; zeros between non-zero digits are significant; leading zeros are not; trailing zeros after a decimal point are significant. For a derived quantity, the result should be rounded to the least number of significant figures among the measured quantities used.

Error propagation: for a quantity like Z = A^p B^q, the relative error adds: ΔZ/Z = p(ΔA/A) + q(ΔB/B).

2 Kinematics

For uniformly accelerated motion: v = u + at, s = ut + ½at², v² = u² + 2as. Relative velocity of A with respect to B is v_A − v_B (as vectors).

Projectile motion launched at angle θ with speed u: time of flight T = 2u sinθ / g, maximum height H = u²sin²θ / 2g, range R = u²sin2θ / g. Range is maximum at θ = 45°, and the same range occurs for complementary angles (e.g. 30° and 60°).

3 Laws of Motion

Newton's first law: a body stays at rest or in uniform motion unless acted on by a net external force (inertia). Second law: F = ma (more precisely, F = dp/dt). Third law: every action has an equal and opposite reaction — this is what explains rocket propulsion, since the rocket and expelled exhaust gas exert equal, opposite forces on each other.

On a frictionless incline of angle θ, a block's acceleration along the incline is g sinθ. Friction: kinetic friction f = μN. The angle of repose (maximum incline angle before sliding starts on its own) satisfies tanθ = μ.

4 Work, Energy and Power

Work done by a force: W = F·d cosθ — note a force perpendicular to displacement (like centripetal force in uniform circular motion) does zero work. Work-energy theorem: net work done equals the change in kinetic energy.

KE = ½mv², gravitational PE = mgh. In an elastic collision, both momentum and kinetic energy are conserved; in an inelastic collision, only momentum is conserved — some KE converts to heat/sound/deformation. Power is the rate of doing work: P = W/t, unit watt (J/s).

5 Rotational Motion

Torque τ = r × F is the rotational analogue of force. Moment of inertia (I) is the rotational analogue of mass — it depends on both mass and how that mass is distributed relative to the axis (e.g. a solid sphere about its diameter: I = ⅖MR²; a solid cylinder about its axis: I = ½MR²).

Angular momentum L = Iω is conserved when no external torque acts — this is why a spinning figure skater speeds up when pulling their arms in (I decreases, so ω must increase to keep L constant). For rolling without slipping, v = ωR.

6 Gravitation

Newton's law of gravitation: F = Gm₁m₂/r². Escape velocity from a planet's surface: vₑ = √(2gR) — for Earth, roughly 11.2 km/s. Orbital velocity for a satellite close to the surface: v₀ = √(gR), and it can be shown that vₑ = √2 × v₀.

Kepler's second law (equal areas in equal times) is equivalent to conservation of angular momentum, since gravity is a central force. Gravitational acceleration decreases both with height above the surface and with depth below it.

7 Properties of Solids and Liquids

Young's modulus Y = stress/strain (unit: Pa). Bernoulli's principle: along a streamline, as fluid speed increases, pressure decreases — this is why airflow speeds up over a narrowed pipe section while pressure drops (the Venturi effect).

A falling object in a viscous fluid reaches terminal velocity when the net force is zero — viscous drag plus buoyancy balance weight. Surface tension causes capillary rise h = 2Tcosθ / (rρg) — a narrower tube gives a greater rise.

8 Thermodynamics

First law: ΔQ = ΔU + ΔW — heat added equals the change in internal energy plus work done by the system. In an adiabatic process, ΔQ = 0, so ΔU = −ΔW. In an isothermal process for an ideal gas, temperature (and so internal energy) doesn't change, so ΔU = 0.

A Carnot engine's efficiency η = 1 − T₂/T₁ depends only on the hot and cold reservoir temperatures, not on the working substance — no real engine operating between the same two temperatures can be more efficient.

9 Kinetic Theory of Gases

Ideal gas law: PV = nRT. Average kinetic energy per molecule is 3/2 kT — it depends only on temperature, not on the identity of the gas. RMS speed v_rms = √(3RT/M), so it scales with √T.

Mayer's relation: Cₚ − Cᵥ = R. Degrees of freedom for a monoatomic gas = 3 (translational only); diatomic gases add rotational degrees of freedom, changing their specific heats.

10 Oscillations and Waves

Simple harmonic motion: x = A sin(ωt + φ), period T = 2π/ω. At the mean position, velocity is maximum and acceleration is zero; at the extremes, it's the reverse. A simple pendulum's period T = 2π√(L/g) is independent of the mass on the string.

Wave speed v = fλ — at constant speed, doubling frequency halves wavelength. The Doppler effect: apparent frequency increases as a source approaches an observer, and decreases as it recedes.

11 Electrostatics

Coulomb's law: F = kq₁q₂/r². Inside a conductor in electrostatic equilibrium, the electric field is always zero — any excess charge resides on the surface. Electric potential due to a point charge, V = kq/r, decreases with distance.

Parallel plate capacitor: C = ε₀A/d. Capacitors in series combine like resistors in parallel (equivalent capacitance is less than the smallest individual value); capacitors in parallel simply add.

12 Current Electricity

Ohm's law: V = IR. Resistors in series: equivalent resistance is the sum. Resistors in parallel: reciprocals add. Kirchhoff's current law (junction rule) follows directly from conservation of charge; Kirchhoff's voltage law (loop rule) follows from conservation of energy.

Power dissipated in a resistor: P = I²R = V²/R. For most metallic conductors, resistance increases with temperature.

13 Magnetic Effects of Current and Magnetism

The direction of the magnetic field around a straight current-carrying wire follows the right-hand thumb rule. Force on a moving charge: F = qvB sinθ — a charge moving parallel to the field experiences zero force. Magnetic field at the center of a circular current loop: B = μ₀I/2R.

A cyclotron uses a magnetic field to bend charged particles into a circular path while an alternating electric field accelerates them across the gap each half-cycle.

14 Electromagnetic Induction and Alternating Currents

Faraday's law: induced EMF = −dΦ/dt — it depends on the rate of change of flux, not the flux itself. Lenz's law (the induced current opposes the change that caused it) is a direct consequence of conservation of energy.

RMS value of an AC signal = peak/√2. In an LCR circuit at resonance, inductive and capacitive reactance cancel, so impedance is at its minimum and purely resistive.

15 Electromagnetic Waves

EM waves are produced by accelerating charges and are transverse — the electric field E and magnetic field B oscillate perpendicular to each other and to the direction of propagation, in phase. In vacuum, all EM waves travel at speed c, independent of frequency.

The EM spectrum in order of increasing wavelength: gamma rays → X-rays → ultraviolet → visible light → infrared → microwaves → radio waves.

16 Optics

Mirror formula: 1/v + 1/u = 1/f. Total internal reflection occurs when light travels from a denser to a rarer medium at an angle of incidence greater than the critical angle. In Young's double-slit experiment, fringe width β = λD/d.

A convex lens forms a real image when the object is placed beyond the focal length. Diffraction effects are most pronounced when the size of the aperture or obstacle is comparable to the wavelength of light.

17 Dual Nature of Matter and Radiation

Einstein's photoelectric equation: KE_max = hf − φ, where φ is the work function (minimum energy needed to eject an electron from the metal surface). Below the threshold frequency, no photoelectrons are emitted no matter how intense the light — intensity affects the number of photoelectrons, not their maximum kinetic energy, which depends only on frequency.

De Broglie wavelength: λ = h/p — inversely proportional to momentum, so it applies to matter as well as light.

18 Atoms and Nuclei

In the Bohr model, the energy of an electron in the nth orbit of hydrogen: Eₙ = −13.6/n² eV. Half-life is the time for half of a radioactive sample to decay; activity decreases exponentially with time.

Binding energy per nucleon is highest around iron (mass number ≈56) — this is why fusion releases energy for light nuclei combining toward iron, and fission releases energy for heavy nuclei splitting toward it.

19 Electronic Devices

A p-n junction diode offers low resistance in forward bias and high resistance in reverse bias. A full-wave rectifier needs a minimum of 2 diodes with a center-tapped transformer (or 4 in a bridge configuration without one).

In an n-type semiconductor, electrons are the majority charge carriers (holes are majority in p-type). NAND is a universal gate — any other logic gate can be built from NAND gates alone.

20 Communication Systems

Modulation superimposes a low-frequency message signal onto a high-frequency carrier — necessary mainly because antennas of a practical size can only efficiently transmit signals at high frequency. In amplitude modulation (AM), the carrier's amplitude varies with the message signal; frequency modulation (FM) varies the carrier's frequency instead and is generally less susceptible to noise.

Sky wave propagation relies on the ionosphere reflecting radio waves back to Earth, extending range beyond line of sight.