NEET 2025 • Class XII Physics

NCERT 2025–26: Class 12 Physics Hub — Notes, Figures, Summaries, Quizzes & Downloads

This hub brings together all nine NCERT units — Electrostatics; Current Electricity; Magnetic Effects of Current & Magnetism; Electromagnetic Induction & Alternating Currents; Electromagnetic Waves; Optics; Dual Nature of Radiation & Matter; Atoms & Nuclei; and Electronic Devices — with chapters 1–14 presented in a consistent, exam-ready format. Every chapter block follows the same layout: Notes → Figures → Quick Summary → 10-MCQ Quiz → Downloads. Use the sticky contents at left to jump between chapters, and the search box to filter chapters live on this page.

Syllabus verified • Updated: 06 Sep 2025

Unit Overview

This page is your master table of contents for NCERT Class XII Physics. Units are ordered exactly as in NCERT, and each chapter block is self-contained for teaching and revision: topic-wise notes (definitions, laws, derivations), diagram callouts (field lines, circuits, ray diagrams), a quick summary for last-minute revision, a 10-MCQ quiz for NEET/Boards pattern practice, and downloads (formula sheets, derivation checklists, circuit maps). Progress chips flag weightage (High/Medium), numerical/derivation density, and PYQ focus to help you prioritise.

High-yield PYQs Derivation checklists Circuit & ray diagrams Quick formula sheets

01 Electric Charges and Fields

Electrostatics Weightage: High Updated: 09 Sep 2025
Chapter Notes
  • Electric charge & electrification: Rubbing transfers electrons between materials → one becomes +ve (loss of e⁻), the other −ve (gain of e⁻). Like charges repel, unlike attract. Gold-leaf electroscope detects charge by leaf divergence.
  • Conductors, insulators, semiconductors: Conductors (metals, body, Earth) let charge move and spread over the surface; insulators (glass, plastic, wood) hold charge where placed; semiconductors have intermediate behaviour.
  • Basic properties of charge:
    • Additivity: algebraic sum of all charges.
    • Conservation: total charge of an isolated system is constant (transfer, not creation).
    • Quantisation: q = n e, where e = 1.602×10−19 C (magnitude of charge on electron/proton). For macroscopic amounts, charge appears continuous.
  • Coulomb’s law (point charges in vacuum): F = \(\dfrac{1}{4\pi\varepsilon_0}\)\(\dfrac{|q_1 q_2|}{r^2}\) along the line joining the charges; repulsive for like, attractive for unlike. Vector form on q₂ due to q₁: \(\vec F_{21} = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q_1 q_2}{r_{21}^2}\,\hat r_{21}\). Superposition principle: net force is vector sum of pairwise forces.
  • Electric field \(\vec E\): Field at a point is force per unit positive test charge, \(\vec E = \vec F/q_0\). For point charge Q, \(\vec E = \dfrac{1}{4\pi\varepsilon_0}\dfrac{Q}{r^2}\hat r\) (radially outwards for +Q, inwards for −Q). Fields add vectorially (superposition).
  • Field lines (Faraday): Start on + charges and end on − charges (or infinity), never cross, are denser where field is stronger, and do not form closed loops in electrostatics.
  • Electric flux \(\Phi\): Through a small area \(\Delta S\): \(\Delta \Phi = \vec E\cdot \Delta \vec S = E\,\Delta S \cos\theta\). For a surface, \(\Phi = \int \vec E\cdot d\vec S\). Unit: N·m²·C⁻¹.
  • Dipole \((+q, -q)\) & dipole moment: \(\vec p = q(2a)\,\hat p\) (from − to +). Far field (\(r \gg a\)): on-axis \(E \approx \dfrac{1}{4\pi\varepsilon_0}\dfrac{2p}{r^3}\), on equatorial line \(E \approx -\dfrac{1}{4\pi\varepsilon_0}\dfrac{p}{r^3}\). In uniform \(\vec E\): net force = 0, torque \(\vec \tau = \vec p \times \vec E\) tends to align \(\vec p\) with \(\vec E\).
  • Continuous charge: Linear density \(\lambda\) (C·m⁻¹), surface density \(\sigma\) (C·m⁻²), volume density \(\rho\) (C·m⁻³). Field found by integrating contributions of small charge elements using Coulomb’s law + superposition.
  • Gauss’s law: Total flux through any closed surface S equals enclosed charge over \(\varepsilon_0\): \(\displaystyle \oint_S \vec E\cdot d\vec S = \dfrac{q_{\text{enc}}}{\varepsilon_0}\). Very powerful with symmetry:
    • Infinite line charge (\(\lambda\)): \(E = \dfrac{\lambda}{2\pi \varepsilon_0 r}\), radial.
    • Infinite plane sheet (\(\sigma\)): \(E = \dfrac{\sigma}{2\varepsilon_0}\), uniform & ⟂ to sheet.
    • Thin spherical shell (charge \(q\)): outside: \(E = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r^2}\); inside: 0.
  • NEET Focus: Coulomb’s law & superposition; point-field and field lines basics; flux definition; dipole field & \(\tau = pE\sin\theta\); Gauss’s law shortcuts (line, sheet, shell).
Important Figures
Two point charges with force vectors showing attraction/repulsion and vector addition
Coulomb’s law and superposition of forces on a test charge.
Electric field lines for a dipole showing direction and density
Field lines: start on +, end on −; density ∝ field strength; never cross.
Gaussian surfaces: cylinder for line charge, pillbox for sheet, sphere for shell
Gauss’s law with symmetry: line (cylinder), sheet (pillbox), shell (sphere).
Quick Summary

Charges come in ±, add algebraically, and are conserved/quantised (q=ne). Static forces obey Coulomb’s inverse-square law and superpose. The electric field \(\vec E\) guides forces and flux; field lines visualise direction/strength. Dipoles feel a torque \(\vec\tau=\vec p\times\vec E\). Gauss’s law converts symmetry into quick fields: \(E_{\text{line}}=\lambda/(2\pi\varepsilon_0 r)\), \(E_{\text{sheet}}=\sigma/(2\varepsilon_0)\), and a charged shell acts like a point charge outside but gives \(E=0\) inside.

Practice Quiz (10 MCQs)
Downloads
Coulomb’s Law & Superposition — Formula Sheet (PDF) Field Lines & Flux Quick Charts (PNG) Gauss’s Law Applications — Summary (PDF)
Cross-links

Continue with: Electrostatic Potential & Capacitance · Back to hub

02 Electrostatic Potential & Capacitance

Electrostatics Weightage: High Updated: 09 Sep 2025
Chapter Notes
  • Potential energy (conservative fields): Work done against Coulomb force is path–independent. For moving a test charge from R to P, $$\Delta U = U_P - U_R = W_{R\to P} \,.$$ Zero reference is often chosen at infinity.
  • Electrostatic potential $V$: Work per unit positive test charge: $$V_P - V_R = \frac{U_P - U_R}{q_0}, \qquad \vec E = -\nabla V \ \ (\text{in 1D: } E = -\frac{dV}{dl}).$$ Units: volt (V) = J·C$^{-1}$.
  • Potentials for common sources:
    • Point charge $Q$: $ \displaystyle V(r) = \frac{1}{4\pi\varepsilon_0}\frac{Q}{r} $ (choose $V(\infty)=0$).
    • Dipole $\vec p$ (far field): $ \displaystyle V(r,\theta) = \frac{1}{4\pi\varepsilon_0}\frac{p\cos\theta}{r^2} $; zero on equatorial plane.
    • Uniformly charged thin spherical shell (charge $q$, radius $R$): outside $r\ge R$: $ \displaystyle V=\frac{1}{4\pi\varepsilon_0}\frac{q}{r}$; inside $r\le R$: $ \displaystyle V=\frac{1}{4\pi\varepsilon_0}\frac{q}{R}$ (constant).
    • System/continuous charge: Add algebraically (superposition) or integrate: $V=\int \frac{1}{4\pi\varepsilon_0}\frac{dq}{r}$.
  • Equipotential surfaces: $V=\text{constant}$ surfaces; $\vec E$ is normal to them and points toward decreasing $V$. Magnitude along normal: $|\vec E|= -\,dV/dl$.
  • Potential energy of charges:
    • Two charges: $ \displaystyle U = \frac{1}{4\pi\varepsilon_0}\frac{q_1 q_2}{r_{12}} $ (positive for like, negative for unlike).
    • Many charges: $ \displaystyle U = \frac{1}{4\pi\varepsilon_0}\sum_{i
    • In external potential $V(\mathbf r)$: single charge $U=qV$, dipole $U=-\vec p\cdot \vec E$.
    • Energy unit: $1\,\text{eV}=1.602\times10^{-19}$ J.
  • Conductors (electrostatics): Inside $E=0$; excess charge on surface; surface field $E=\sigma/\varepsilon_0$ (outward normal); $V$ is constant throughout conductor; cavities are shielded (no internal $E$ if no enclosed charge).
  • Dielectrics & polarisation: In linear, isotropic media $ \vec P = \varepsilon_0 \chi_e \vec E $, with dielectric constant $K=1+\chi_e$ and permittivity $\varepsilon=K\varepsilon_0$. Insertion reduces field and raises capacitance.
  • Capacitors: Two conductors separated by an insulator. Capacitance $C = Q/V$ depends on geometry and medium.
    • Parallel plates (vacuum): $ \displaystyle C_0=\frac{\varepsilon_0 A}{d}$, field $E=\frac{\sigma}{\varepsilon_0}=\frac{Q}{A\varepsilon_0}$.
    • With dielectric $K$ fully filling gap: $ \displaystyle C=K C_0 = \frac{K\varepsilon_0 A}{d}$.
    • Series: $ \displaystyle \frac{1}{C_\text{eq}}=\sum \frac{1}{C_i}$; same $Q$.
    • Parallel: $ \displaystyle C_\text{eq}=\sum C_i$; same $V$.
  • Energy in capacitor / field: $$U=\tfrac12 QV=\tfrac12 CV^2=\tfrac12 \frac{Q^2}{C}, \qquad u=\tfrac12 \varepsilon E^2 \ \ (\text{energy density}).$$
  • NEET Focus: $V$ for point/dipole/shell; $E=-dV/dl$ and $E\perp$ equipotentials; $U$ of pairs/system; $C=\varepsilon A/d$ and dielectric factor $K$; series/parallel rules; $U=\tfrac12 CV^2$, $u=\tfrac12\varepsilon E^2$; conductor rules (shielding, $E=\sigma/\varepsilon_0$).
Important Figures
Equipotential surfaces around a point charge with electric field lines normal to them
Equipotentials are ⟂ to $\vec E$; spacing conveys field strength.
Dipole showing angle theta and 1/r^2 potential variation
Dipole potential $V=\frac{1}{4\pi\varepsilon_0}\frac{p\cos\theta}{r^2}$ (far field); zero on equatorial plane.
Parallel plate capacitor with dielectric slab showing increased capacitance
Parallel plates: $C_0=\varepsilon_0A/d$; with dielectric $C=K C_0$.
Quick Summary

Potential is energy per unit charge; use $V=\frac{1}{4\pi\varepsilon_0}\frac{Q}{r}$ (point), dipole $V\propto r^{-2}$, and shells give constant $V$ inside. Field follows $E=-dV/dl$ and is normal to equipotentials. Capacitors store energy $U=\tfrac12 CV^2$; $C$ scales with $\varepsilon$ and geometry, adds inversely in series and directly in parallel.

Practice Quiz (10 MCQs)
1) For a conservative electrostatic force, the work from R to P depends on:
2) Potential at distance $r$ from a point charge $Q$ (with $V(\infty)=0$) is:
3) Along the normal to an equipotential surface, the field magnitude is:
4) Potential energy of two charges $q_1,q_2$ at separation $r$ equals:
5) Inside an isolated conductor in electrostatic equilibrium:
6) Capacitance of a parallel-plate capacitor (vacuum) is:
7) Fully inserting a dielectric of constant $K$ between the plates makes:
8) Two capacitors $C_1$ and $C_2$ in series have equivalent capacitance:
9) Energy stored in a capacitor can be written as:
10) Potential energy of a dipole in a uniform field is:
11) Potential at axial point of a dipole (distance $r \gg d$) is:
12) Energy density of electric field in a capacitor is:
Downloads
Potential & Capacitance — Formula Sheet (PDF) Series/Parallel Capacitors — Quick Guide (PNG) Field Energy & Dielectrics — Summary (PDF)
Cross-links

Continue with: Current Electricity · Electric Charges & Fields (revision)

03 Current Electricity

DC Circuits Weightage: High Updated: 10 Sep 2025
Chapter Notes
  • Electric current: Rate of flow of charge. Instantaneous current $I=\dfrac{dQ}{dt}$; for steady flow $I = Q/t$. SI unit: ampere (A).
  • Currents in conductors: Metals have mobile electrons (negative carriers); lattice ions are fixed. With no $\vec E$, random thermal motion ⇒ zero net current. A source (cell) maintains $\vec E$ and drives steady current.
  • Ohm’s law & resistance: For ohmic materials, $V\propto I$ ⇒ $V=IR$. Resistance $R=\rho \dfrac{l}{A}$ (material property $\rho$: resistivity). Current density $j=\dfrac{I}{A}$. Microscopic form: $j=\sigma E$ or $E=\rho j$ ($\sigma=1/\rho$).
  • Drift & origin of resistivity: Electrons accelerate under $\vec E$ but collide ⇒ steady drift velocity $v_d=\dfrac{-eE\tau}{m}$ (magnitude $eE\tau/m$). Current density $j = n q v_d$ (for electrons $j=-ne v_d$). Conductivity $\sigma=\dfrac{ne^2\tau}{m}$; resistivity $\rho=\dfrac{m}{ne^2\tau}$.
  • Limits of Ohm’s law: Non-ohmic devices/materials show non-linear $V$–$I$, polarity dependence (e.g., diode), or multivalued characteristics (e.g., GaAs under certain conditions).
  • Resistivity ranges: Metals $\sim10^{-8}$–$10^{-6}\ \Omega\,$m; insulators enormously larger; semiconductors in-between and tunable (doping, temperature).
  • Temperature dependence: Metals: $\rho_T=\rho_0[1+\alpha(T-T_0)]$ (approximately linear increase). Semiconductors: $\rho$ decreases with $T$ (carrier density increases). Alloys (e.g., Nichrome) have weak $T$-dependence ⇒ stable standard resistors.
  • Electrical power & energy: Power $P=IV = I^2R = \dfrac{V^2}{R}$; energy in time $\Delta t$: $\Delta W=IV\Delta t$. Transmission: loss $\propto \left(\dfrac{P}{V}\right)^2 R_c$ ⇒ use high $V$ to reduce cable losses.
  • Cells, emf, internal resistance: Emf $\varepsilon$ is open-circuit potential. With current $I$ through external $R$ and internal $r$: terminal voltage $V=\varepsilon - Ir$, current $I=\dfrac{\varepsilon}{R+r}$.
  • Cells in series/parallel: Series: $\varepsilon_{\text{eq}}=\sum \varepsilon_i$, $r_{\text{eq}}=\sum r_i$. Parallel (two cells): $\dfrac{1}{r_{\text{eq}}}=\dfrac{1}{r_1}+\dfrac{1}{r_2}$ and $\dfrac{\varepsilon_{\text{eq}}}{r_{\text{eq}}}=\dfrac{\varepsilon_1}{r_1}+\dfrac{\varepsilon_2}{r_2}$.
  • Kirchhoff’s rules: Junction rule (charge conservation): $\sum I_{\text{in}}=\sum I_{\text{out}}$. Loop rule (energy conservation): algebraic sum of potential changes around any closed loop is zero.
  • Wheatstone bridge: Four-resistor network to find unknown resistance. Balance (galvanometer current $=0$) when $\dfrac{R_2}{R_1}=\dfrac{R_4}{R_3}$.
  • NEET Focus: $I=dQ/dt$; $R=\rho l/A$; $j=\sigma E$; $v_d=eE\tau/m$; $P=I^2R=\dfrac{V^2}{R}$; $V=\varepsilon - Ir$; series/parallel of cells; KCL/KVL; Wheatstone balance condition.
Important Figures
Electron drift with collisions under an applied electric field
Drift under $\vec E$: small $v_d$ superposed on random motion; collisions set $\tau$.
Current density proportional to electric field in a conductor
Microscopic Ohm’s law: $j=\sigma E$; macroscopically $V=IR$.
Wheatstone bridge showing R1,R2,R3,R4 and galvanometer between the midpoints
Wheatstone bridge balance: $R_2/R_1 = R_4/R_3$ (no galvanometer current).
Quick Summary

Current is charge flow rate ($I=dQ/dt$). Ohm’s law $V=IR$ links $V$, $I$, $R$; $R=\rho l/A$. Microscopically, $j=\sigma E$ with $\sigma=ne^2\tau/m$ and drift $v_d=eE\tau/m$. Power loss $P=I^2R$. Real cells have internal resistance: $V=\varepsilon -Ir$. Use Kirchhoff’s rules for complex circuits and the Wheatstone bridge for precise resistance measurement.

Practice Quiz (10 MCQs)
1) Relation among current $I$, charge density $n$, charge $q$, cross-section $A$, and drift velocity $v_d$ is:
2) Ohm’s law states that (at constant physical conditions):
3) For metals, resistivity $\rho$ typically:
4) Two resistors $R_1$ and $R_2$ in parallel have equivalent resistance:
5) A cell of emf $\varepsilon$ and internal resistance $r$ delivers current $I$. Terminal voltage is:
6) Kirchhoff’s junction rule expresses conservation of:
7) In a balanced Wheatstone bridge, the condition is:
8) Potentiometer principle used for comparing emfs relies on:
9) Electrical power dissipated in a resistor is:
10) $n$ identical cells (each $\varepsilon$, $r$) in series have equivalent:
Downloads
Current Electricity — Formula Sheet (PDF) Kirchhoff & Wheatstone Bridge — Quick Guide (PNG) Power, EMF & Internal Resistance — Problem Set (PDF)
Cross-links

Continue with: Moving Charges & Magnetism · Electrostatic Potential & Capacitance (revision)

04 Moving Charges & Magnetism

Magnetism of Currents Weightage: High Updated: 10 Sep 2025
Chapter Notes
  • Oersted’s discovery: A current in a wire deflects a nearby compass ⇒ currents produce magnetic fields $\vec B$ (circles around the wire; reverse current ⇒ reverse deflection).
  • Lorentz force: On charge $q$ moving with velocity $\vec v$ in fields $\vec E,\vec B$, $$\vec F = q\big(\vec E + \vec v \times \vec B\big).$$ Magnetic part $q(\vec v\times\vec B)$ is $\perp$ to both $\vec v$ and $\vec B$ ⇒ does no work; zero if $v=0$ or $\vec v \parallel \vec B$. SI unit of $B$: tesla (T); $1\,\text{G} = 10^{-4}\,\text{T}$.
  • Force on a current element: Straight conductor of vector length $\vec l$ carrying current $I$ in external $\vec B$ feels $$\vec F = I\,\vec l \times \vec B.$$
  • Motion in uniform $\vec B$: For $\vec v \perp \vec B$: circular motion, radius $r=\dfrac{m v}{|q|B}$; cyclotron (angular) frequency $\omega=\dfrac{|q|B}{m}$ (independent of $v$). With a component $\parallel \vec B$ ⇒ helical path.
  • Biot–Savart law: Field $d\vec B$ at $P$ due to current element $I\,d\vec l$ at separation $r$: $$d\vec B = \frac{\mu_0}{4\pi}\,\frac{I\,d\vec l \times \hat r}{r^2} \;=\; \frac{\mu_0}{4\pi}\,\frac{I\,d\vec l \times \vec r}{r^3}.$$ Superposition holds (vector addition of contributions).
  • Field on axis of a circular loop (radius $R$, current $I$): $$B(x) = \frac{\mu_0 I R^2}{2\,(x^2+R^2)^{3/2}}, \qquad B(0)=\frac{\mu_0 I}{2R}.$$ Direction by right-hand rule (curl fingers with current; thumb gives $\vec B$ on axis).
  • Ampere’s circuital law: $$\oint_C \vec B\cdot d\vec l = \mu_0 I_{\text{enc}}.$$ Long straight wire: $B(r)=\dfrac{\mu_0 I}{2\pi r}$ (circles around wire; right-hand grip rule).
  • Solenoid (long): Nearly uniform field inside, negligible outside: $$B = \mu_0 n I \quad (n=\text{turns per unit length}).$$
  • Two parallel currents: Like (same direction) ⇒ attract; unlike ⇒ repel. Force per unit length: $$\frac{F}{\ell} = \frac{\mu_0 I_a I_b}{2\pi d}.$$
  • Current loop as magnetic dipole: Magnetic moment $\vec m = N I \vec A$ (direction by right-hand rule). Torque in uniform field: $$\vec\tau = \vec m \times \vec B, \qquad \tau = N I A B \sin\theta.$$
  • Moving-coil galvanometer: Torque $=N I A B$, balanced by spring $k\phi$ ⇒ deflection $$\phi = \frac{NAB}{k}\,I.$$ Make an ammeter with a shunt (small $r_s$ in parallel); make a voltmeter with a large series resistor $R$.
  • NEET Focus: Lorentz force; $r=\dfrac{mv}{|q|B}$ and $\omega=\dfrac{|q|B}{m}$; Biot–Savart basics; $B$ of long wire/loop/solenoid; Ampere’s law; $F/\ell$ between wires; $\tau=N I A B\sin\theta$; galvanometer → ammeter/voltmeter.
Important Figures
Lorentz force on a moving charge showing v cross B perpendicular to both
Lorentz force: $\vec F=q(\vec E+\vec v\times\vec B)$ is $\perp$ to $\vec v$ and $\vec B$ (no work).
Biot–Savart geometry and axial magnetic field of a circular loop
Biot–Savart: $d\vec B \propto I\,d\vec l \times \hat r/r^2$; loop axis: $B(x)=\dfrac{\mu_0 I R^2}{2(x^2+R^2)^{3/2}}$.
Field inside a long solenoid and forces between parallel currents
Solenoid: $B=\mu_0 n I$ (uniform inside). Parallel currents: $F/\ell=\mu_0 I_a I_b/(2\pi d)$.
Quick Summary

Moving charges create magnetic fields. Use Lorentz force for particle motion; Biot–Savart and Ampere’s law to compute $\vec B$ (wire, loop, solenoid). Parallel currents attract/repel with $F/\ell=\mu_0 I_a I_b/(2\pi d)$. Current loops behave as dipoles ($\vec m=NIA\,\hat n$) with torque $\vec\tau=\vec m\times\vec B$. Galvanometers exploit this torque and become ammeters (shunt) or voltmeters (series resistor).

Practice Quiz (10 MCQs)
Downloads
Biot–Savart & Ampere — Formula Sheet (PDF) Loop/Solenoid Fields — Quick Charts (PNG) Galvanometer→Ammeter/Voltmeter — Guide (PDF)
Cross-links

Continue with: Magnetism & Matter · Current Electricity (revision)

05 Magnetism & Matter

Conceptual Weightage: Medium–High Updated: 10 Sep 2025
Chapter Notes
  • Introduction: Magnetism has been known since ancient times (Magnesia). Modern view: circulating/moving charges (currents) underlie magnetic effects.
  • Fundamentals about magnets:
    • Earth as a magnet: behaves approximately like a huge bar magnet (north–south alignment).
    • Poles: a freely suspended bar magnet aligns N–S; like poles repel, unlike attract.
    • No magnetic monopoles: breaking a magnet gives two smaller magnets, each with N and S. (Contrast with isolated electric charges.)
  • Bar magnet & field lines: Iron filings show $\vec B$-lines:
    • Form continuous closed loops (outside N→S; inside S→N).
    • Tangent gives local direction of $\vec B$; density indicates strength.
    • Field lines never intersect.
    • Equivalent solenoid picture: A bar magnet ≈ current-carrying solenoid (at large distances behaves like a magnetic dipole).
  • Dipole in uniform field: $$\vec\tau = \vec m \times \vec B,\qquad U = -\,\vec m\cdot \vec B = -\,mB\cos\theta.$$ Stable equilibrium: $\vec m \parallel \vec B$ ($\theta=0^\circ$). Unstable: $\vec m \anti \vec B$ ($\theta=180^\circ$).
  • Gauss’s law for magnetism: $$\oint_S \vec B \cdot d\vec S = 0.$$ Net magnetic flux through any closed surface is zero ⇒ magnetic field lines have no start/end points (no monopoles).
  • Magnetisation & magnetic intensity:
    • Magnetisation (per unit volume): $\vec M$ (A·m$^{-1}$).
    • Magnetic intensity: $\vec H$; total field in matter: $$\vec B = \mu_0(\,\vec H + \vec M\,).$$
    • Magnetic susceptibility: $\chi$ with $\vec M = \chi\,\vec H$ (linear, isotropic materials).
    • Relative permeability: $\mu_r = 1+\chi$; permeability: $\mu=\mu_0\mu_r=\mu_0(1+\chi)$.
  • Magnetic properties of materials:
    • Diamagnetic: very weakly repelled; $\chi$ small negative ($\chi<0$), $\mu<\mu_0$. Induced moments oppose applied field. (e.g., Bi, Cu, water). Superconductors → perfect diamagnets (Meissner effect).
    • Paramagnetic: weakly attracted; $\chi$ small positive ($\chi>0$), $\mu>\mu_0$. Permanent atomic dipoles partially align in $\vec B$; effect stronger at low $T$ (thermal disorder competes).
    • Ferromagnetic: strongly attracted; $\chi\!\gg\!1$, large $\mu$. Domain formation/alignment causes strong magnetisation; hard materials retain magnetisation (permanent magnets), soft lose it (good cores). Above Curie temperature $T_C$, becomes paramagnetic.
  • NEET Focus: Closed-loop $\vec B$-lines vs electrostatics; dipole $\vec\tau$, $U$; $\oint \vec B\cdot d\vec S=0$; $\vec B=\mu_0(\vec H+\vec M)$, $\vec M=\chi\vec H$, $\mu_r=1+\chi$; dia/para/ferro traits & examples; Curie temperature idea.
Important Figures
Bar magnet with closed magnetic field lines looping from north to south outside and back inside
Bar magnet: closed $\vec B$-loops (contrast with electric field lines).
Magnetic dipole in uniform field showing torque and energy minima
Dipole: $\vec\tau=\vec m\times\vec B$, $U=-\vec m\cdot\vec B$; stable when $\vec m\parallel \vec B$.
Illustration of diamagnetic repulsion, paramagnetic attraction, and ferromagnetic domain alignment
Dia vs para vs ferro: sign of $\chi$ and qualitative response to $\vec B$.
Quick Summary

Magnetic field lines form closed loops (no monopoles). A magnetic dipole feels $\vec\tau=\vec m\times\vec B$ and has $U=-\vec m\cdot\vec B$. In matter, $\,\vec B=\mu_0(\vec H+\vec M)$ with $\,\vec M=\chi\vec H$ and $\,\mu_r=1+\chi$. Diamagnets ($\chi<0$) are weakly repelled; paramagnets ($\chi>0$ small) are weakly attracted; ferromagnets ($\chi\!\gg\!1$) show domain-driven strong magnetisation and lose it above $T_C$.

Practice Quiz (10 MCQs)
Downloads
Magnetism & Matter — Formula & Concept Sheet (PDF) Dia/Para/Ferro Comparison Table (PNG) Dipole Energy & Torque Problems (PDF)
Cross-links

Continue with: Electromagnetic Induction · Moving Charges & Magnetism (revision)

06 Electromagnetic Induction

Core Concepts Weightage: High Updated: 10 Sep 2025
Chapter Notes
  • Idea: Changing magnetic flux through a circuit induces an emf and (if closed) a current. Faraday & Henry’s experiments showed that relative motion or a time-varying current/field produces induction.
  • Magnetic flux: For a flat area $A$ in uniform $\vec B$, $$\Phi_B = \vec B\cdot \vec A = BA\cos\theta,$$ SI unit: weber (Wb) = T·m$^2$. Change flux by varying $B$, $A$, or angle $\theta$.
  • Faraday’s law: $$\varepsilon = -\,\frac{d\Phi_B}{dt}, \qquad \varepsilon_{\text{coil}} = -\,N\frac{d\Phi_B}{dt}.$$ If circuit has resistance $R$, induced current $I=\varepsilon/R$.
  • Lenz’s law (direction): The induced emf/current opposes the change in flux that produces it (energy conservation). Approaching N-pole ⇒ induced N facing it (repel); receding N-pole ⇒ induced S (attract).
  • Motional emf: A conductor of length $l$ moving with speed $v$ ⟂ to uniform $B$ develops $$\varepsilon = B\,l\,v.$$ Origin: Lorentz force separates charges along the rod.
  • Inductance: Flux linkage $\Lambda=N\Phi_B \propto I$.
    • Mutual inductance $M$: Changing $I_2$ induces emf in coil 1: $$\varepsilon_1 = -\,M\,\frac{dI_2}{dt}, \quad M_{12}=M_{21}=M.$$
    • Self-inductance $L$: Changing $I$ in a coil induces back emf: $$\varepsilon = -\,L\,\frac{dI}{dt}, \qquad U=\tfrac12 L I^2.$$ Long solenoid: with $N$ turns, length $l$, area $A$, core $\mu_r$, $$L=\mu_0 \mu_r \frac{N^2 A}{l} = \mu_0\mu_r\,n^2 A\,l \ \ (n=N/l).$$
    • Unit: henry (H).
  • AC generator (application): For a coil of $N$, area $A$ rotating with angular speed $\omega$ in uniform $B$, $$\Phi_B=NBA\cos\omega t,\qquad \varepsilon(t) = -\frac{d\Phi_B}{dt}= \varepsilon_0 \sin\omega t,$$ with peak $\varepsilon_0=NBA\omega$ (alternating polarity ⇒ AC).
  • NEET Focus: $\Phi_B=BA\cos\theta$; $\varepsilon=-N\,d\Phi_B/dt$; Lenz’s law (oppose change); motional emf $Blv$; $M$ reciprocity; $L$ of solenoid; stored energy $U=\tfrac12 LI^2$; generator $\varepsilon_0=NBA\omega$.
Important Figures
Induced current in a coil when a bar magnet approaches or recedes
Faraday’s observations: induced current only when flux through the coil changes.
Conductor sliding on rails in a uniform magnetic field producing motional emf
Motional emf: $\varepsilon=Blv$ from Lorentz force on charges in the moving rod.
Rotating coil in magnetic field producing sinusoidal emf
AC generator: $\varepsilon(t)=NBA\omega\sin\omega t$ (sign from Lenz’s law).
Quick Summary

Changing magnetic flux induces emf: $\varepsilon=-N\,d\Phi_B/dt$. Lenz’s law sets the opposing direction. A moving conductor in $B$ gives $\varepsilon=Blv$. Inductors store magnetic energy $U=\tfrac12 LI^2$; solenoids have $L=\mu_0\mu_r N^2A/l$. Rotating coils in $B$ generate AC with peak $\varepsilon_0=NBA\omega$.

Practice Quiz (10 MCQs)
Downloads
EM Induction — Formula Sheet (PDF) Motional EMF & Lenz’s Law — Diagram Pack (PNG) Inductance & AC Generator — Problems (PDF)
Cross-links

Continue with: Alternating Current · Magnetism & Matter (revision)

07 Alternating Current

AC Circuits Weightage: High Updated: 10 Sep 2025
Chapter Notes
  • AC basics: Alternating voltage/current vary sinusoidally and reverse direction: $v=v_m\sin\omega t$, $i=i_m\sin(\omega t+\phi)$. AC is preferred for transmission (transformers enable efficient step-up/step-down).
  • Pure resistor (R): With $v=v_m\sin\omega t$, current $i=i_m\sin\omega t$ (in phase), $i_m=v_m/R$. Average power over a cycle: $$P_{\text{avg}}=\tfrac12 i_m^2 R = VI \quad (\text{using RMS}).$$
  • RMS values: $$V=\frac{v_m}{\sqrt2},\qquad I=\frac{i_m}{\sqrt2}.$$ Use $P=VI=I^2R=V^2/R$ with RMS $V,I$.
  • Phasors: Rotating vectors (angular speed $\omega$) representing amplitudes and phase of sinusoids; aid in adding voltages/currents of different phases.
  • Pure inductor (L): $i$ lags $v$ by $\pi/2$: $$X_L=\omega L,\qquad i_m=\frac{v_m}{X_L},\qquad P_{\text{avg}}=0\ \ (\text{ideal}).$$
  • Pure capacitor (C): $i$ leads $v$ by $\pi/2$: $$X_C=\frac{1}{\omega C},\qquad i_m=\frac{v_m}{X_C},\qquad P_{\text{avg}}=0\ \ (\text{ideal}).$$
  • Series LCR (R–L–C): $$Z=\sqrt{R^2+(X_L-X_C)^2},\quad i_m=\frac{v_m}{Z},\quad \tan\phi=\frac{X_L-X_C}{R}.$$ Inductive if $X_L\!>\!X_C$ (current lags), capacitive if $X_C\!>\!X_L$ (current leads).
  • Resonance (series): Occurs when $X_L=X_C$ (natural frequency) $$\omega_0=\frac{1}{\sqrt{LC}},\quad Z_{\min}=R,\quad i_m=\frac{v_m}{R}\ (\text{maximum}).$$ Basis of tuning circuits (radios/TV).
  • AC power & power factor: $$P_{\text{avg}}=VI\cos\phi,$$ where $\cos\phi$ is the power factor. Pure $R$: $\phi=0$ ($\cos\phi=1$). Pure $L$ or $C$: $\phi=\pi/2$ ($\cos\phi=0$, wattless current). In RLC, only $R$ dissipates power. Low power factor is corrected with shunt capacitors (for inductive loads).
  • Transformers (mutual induction): Ideal relations $$\frac{V_s}{V_p}=\frac{N_s}{N_p},\qquad \frac{I_p}{I_s}=\frac{N_s}{N_p},\qquad V_p I_p = V_s I_s.$$ Step-up: $N_s>N_p$; step-down: $N_s
  • NEET Focus: RMS vs peak; phase in $R$, $L$, $C$; $X_L=\omega L$, $X_C=1/\omega C$; $Z$ and $\tan\phi$; resonance $\omega_0$; $P=VI\cos\phi$; capacitor for power-factor correction; transformer turn/voltage/current ratios.
Important Figures
Phasor diagrams showing in-phase for resistor, current lagging in inductor, and current leading in capacitor
Phasors: $R$ (in-phase), $L$ (current lags $90^\circ$), $C$ (current leads $90^\circ$).
Impedance triangle and resonance curve for series LCR circuit
Series LCR: $Z=\sqrt{R^2+(X_L-X_C)^2}$; resonance at $\omega_0=1/\sqrt{LC}$.
Transformer with primary and secondary windings on iron core
Transformer: $\dfrac{V_s}{V_p}=\dfrac{N_s}{N_p}$, $\dfrac{I_p}{I_s}=\dfrac{N_s}{N_p}$ (ideal).
Quick Summary

Use RMS values for power: $V=v_m/\sqrt2$, $I=i_m/\sqrt2$, $P=VI\cos\phi$. Reactances: $X_L=\omega L$, $X_C=1/(\omega C)$. In series LCR, $Z=\sqrt{R^2+(X_L-X_C)^2}$ and $\tan\phi=(X_L-X_C)/R$; resonance at $\omega_0=1/\sqrt{LC}$. Shunt capacitors improve lagging power factor. Transformers obey $V_s/V_p=N_s/N_p$ and $V_pI_p=V_sI_s$ (ideal).

Practice Quiz (10 MCQs)
Downloads
AC Circuits — Formula & Phasor Sheet (PDF) Resonance & Power Factor — Quick Charts (PNG) Transformer Basics — Worked Examples (PDF)
Cross-links

Continue with: Electromagnetic Waves · Electromagnetic Induction (revision)

08 Electromagnetic Waves

Unifying Idea Weightage: Medium–High Updated: 10 Sep 2025
Chapter Notes
  • Displacement current (Maxwell): Ampère’s law is completed by adding a term due to changing electric flux: $$i_d=\varepsilon_0\frac{d\Phi_E}{dt}, \qquad \oint \vec B\cdot d\vec l=\mu_0\left(I_{\text{cond}}+\varepsilon_0\frac{d\Phi_E}{dt}\right).$$ This fixes the charging-capacitor paradox and makes $\vec E$/$\vec B$ symmetric.
  • Maxwell’s prediction: Time-varying $\vec E$ and $\vec B$ sustain each other and propagate as electromagnetic waves at $$c=\frac{1}{\sqrt{\mu_0\varepsilon_0}}\approx 3\times10^8\ \text{m s}^{-1},$$ implying light is an EM wave (Hertz verified radio waves; Marconi applied them).
  • Sources of EM waves: Accelerated/oscillating charges radiate. Stationary charges (only $\vec E$) or charges in uniform straight-line motion (steady $\vec B$) do not radiate.
  • Nature of EM waves: Transverse; $\vec E \perp \vec B \perp \hat k$ (direction of travel). In vacuum, $$E_0 = c\,B_0,$$ speed $c$; in a medium $v=\dfrac{1}{\sqrt{\mu\varepsilon}}$.
  • Electromagnetic spectrum (long $\lambda$ → short $\lambda$): Radio → Microwaves → Infrared → Visible (700–400 nm) → Ultraviolet → X-rays → $\gamma$-rays. Production & uses: radio (communication), microwaves (radar/ovens), IR (thermal imaging/remote), visible (vision), UV (sterilisation), X-rays (medical imaging), $\gamma$ (nuclear/therapy).
  • NEET Focus: $i_d=\varepsilon_0\,d\Phi_E/dt$; Ampère–Maxwell law; $c=1/\sqrt{\mu_0\varepsilon_0}$; $E_0=cB_0$; $v=1/\sqrt{\mu\varepsilon}$; spectrum order & typical sources/uses; EM waves are transverse.
Important Figures
Charging capacitor with displacement current between plates completing Ampère’s loop
Displacement current completes Ampère’s law in a charging capacitor.
Perpendicular E and B fields with propagation direction forming a right-handed set
EM wave: $\vec E \perp \vec B \perp \hat k$; $E_0=cB_0$ in vacuum.
Continuous electromagnetic spectrum from radio to gamma rays with uses
EM spectrum overview: radio → microwaves → IR → visible → UV → X-ray → $\gamma$.
Quick Summary

Adding displacement current $\varepsilon_0\,d\Phi_E/dt$ to Ampère’s law predicts self-sustaining, transverse EM waves with speed $c=1/\sqrt{\mu_0\varepsilon_0}$ and $E_0=cB_0$. Accelerated charges radiate EM waves. Know spectrum order, production, and core applications from radio to $\gamma$.

Practice Quiz (10 MCQs)
Downloads
Electromagnetic Waves — Formula & Facts (PDF) EM Spectrum — Uses & Ranges (PNG) Maxwell’s Equations — One-pager (PDF)
Cross-links

Continue with: Ray Optics & Optical Instruments · Alternating Current (revision)

09 Ray Optics & Optical Instruments

Geometrical Optics Weightage: High Updated: 10 Sep 2025
Chapter Notes
  • Ray picture: For everyday scales ($\lambda\sim 400$–$750$ nm $\ll$ object size), light travels in straight lines (rays). Speed in vacuum $c\approx 3\times10^8$ m·s$^{-1}$.
  • Reflection (spherical mirrors): Laws: $i=r$; incident ray, reflected ray, and normal are coplanar.
    Key terms: pole $P$, principal axis, centre of curvature $C$, focus $F$, focal length $f$ ($f=R/2$).
    Mirror formula: $\,\dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}\,,\qquad m=\dfrac{h'}{h}=-\dfrac{v}{u}$.
  • Refraction & Snell’s law: $n_1\sin i=n_2\sin r$. Optically denser medium ⇒ smaller speed ⇒ ray bends towards normal. Apparent depth: objects under water appear raised.
  • Total internal reflection (TIR): From denser to rarer with $i>i_c$, where $\sin i_c=\dfrac{n_{\text{rarer}}}{n_{\text{denser}}}$. Uses: prisms, optical fibres, mirage, diamond brilliance.
  • Refraction at spherical surface: $\,\dfrac{n_2}{v}-\dfrac{n_1}{u}=\dfrac{n_2-n_1}{R}$.
  • Thin lenses:
    • Lens maker (air): $\,\dfrac{1}{f}=(n-1)\!\left(\dfrac{1}{R_1}-\dfrac{1}{R_2}\right)$.
    • Thin lens (Cartesian): $\,\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}$, $\,m=\dfrac{v}{u}$.
    • Power: $P=1/f$ (metre), dioptre (D); $P>0$ converging, $P<0$ diverging.
    • Lenses in contact: $P_{\text{eq}}=\sum P_i$, $\,1/f_{\text{eq}}=\sum 1/f_i$.
  • Prisms: Deviation $\delta=i+e-A$; minimum deviation $D_m$ when $i=e$; $\,n=\dfrac{\sin\!\big((A+D_m)/2\big)}{\sin(A/2)}$; thin prism $\delta\approx(n-1)A$.
  • Optical instruments:
    • Simple microscope: $m=1+\dfrac{D}{f}$ (at near point), $m=\dfrac{D}{f}$ (at infinity).
    • Compound microscope: $m\approx\dfrac{L}{f_o}\cdot\dfrac{D}{f_e}$ (image at infinity).
    • Refracting telescope: $|m|=\dfrac{f_o}{f_e}$, tube length $f_o+f_e$ (normal adjustment).
    • Reflecting telescope (Cassegrain): No chromatic aberration; compact long focal length.
  • NEET Focus: Mirror/lens formulae & sign convention; Snell’s law; TIR condition & $i_c$; lens maker & power; prism $n$ from $A,D_m$; microscope/telescope relations.
Important Figures
Concave/convex mirror with principal axis, C, F, u, v and sign convention
Spherical mirrors: $f=R/2$ and $\,1/v+1/u=1/f$ (Cartesian signs).
Snell’s law refraction and total internal reflection with critical angle
Snell’s law $n_1\sin i=n_2\sin r$; TIR when $i>i_c$ with $\sin i_c=n_{\rm r}/n_{\rm d}$.
Thin lens ray diagram and prism minimum deviation geometry
Thin lens: $1/v-1/u=1/f$; Prism: $n=\sin\!\big((A+D_m)/2\big)/\sin(A/2)$.
Quick Summary

Use the ray model to analyse reflection, refraction and imaging. Remember mirror/lens equations, TIR condition, prism relations, and instrument formulae (simple/compound microscopes, refracting/reflecting telescopes). Power adds for lenses in contact.

Practice Quiz (10 MCQs)
1) For a spherical mirror of radius $R$, the focal length equals:
2) The mirror equation (Cartesian sign convention) is:
3) Snell’s law at an interface is:
4) Total internal reflection occurs when light goes from:
5) The critical angle $i_c$ for denser ($n_d$) to rarer ($n_r$) is:
6) The thin lens formula (Cartesian) is:
7) In air, the lens maker’s formula is:
8) Power of thin lenses in contact equals:
9) For prism angle $A$ at minimum deviation $D_m$, refractive index is:
10) Angular magnification (magnitude) for a refracting telescope at normal adjustment:
Downloads
Mirror & Lens Formulae — One-pager (PDF) Prisms & TIR — Diagram Pack (PNG) Microscope & Telescope — Quick Sheet (PDF)
Cross-links

Continue with: Wave Optics · Electromagnetic Waves (revision)

10 Wave Optics

Physical Optics Weightage: Medium–High Updated: 10 Sep 2025
Chapter Notes
  • Huygens’ principle & wavefronts: Every point on a wavefront acts as a secondary source; the new wavefront is the envelope of secondary wavelets. Explains reflection & refraction (Snell’s law).
  • Interference (Young’s double slit):
    • Superposition: $E=E_1+E_2$ ⇒ $I=I_1+I_2+2\sqrt{I_1I_2}\cos\delta$.
    • Constructive: path difference $\Delta=m\lambda$; Destructive: $\Delta=(m+\tfrac12)\lambda$.
    • For $I_1=I_2=I_0$: $I=4I_0\cos^2\!\frac{\delta}{2}$; $I_{\max}=4I_0$, $I_{\min}=0$.
    • YDSE fringe width: $\displaystyle \beta=\frac{\lambda D}{d}$ (screen distance $D$, slit separation $d$).
    • Coherence: sources must have same frequency and constant phase difference.
  • Diffraction (single slit):
    • Minima: $a\sin\theta=m\lambda$ ($m=\pm1,\pm2,\dots$); central maximum is widest.
    • Angular width of central maximum: $\displaystyle \Delta\theta \approx \frac{2\lambda}{a}$ (small angles).
    • As slit width $a$ decreases, diffraction broadens.
  • Resolving power & Rayleigh criterion:
    • Two point objects are just resolved when principal maximum of one coincides with first minimum of the other.
    • For a circular aperture: $\displaystyle \theta_{\min}=1.22\,\frac{\lambda}{D}$; larger aperture $D$ ⇒ better resolution.
    • Microscope (limit): $\displaystyle d_{\min}\approx \frac{0.61\,\lambda}{\mu\sin\alpha}$ (NA).
  • Polarisation:
    • Unpolarised light through ideal polariser: $I=\tfrac{I_0}{2}$.
    • Malus’ law (polariser–analyser angle $\theta$): $I=I_0\cos^2\theta$ (for already plane-polarised $I_0$).
    • Brewster’s law: $\tan i_p = n$ (air to medium); reflected & refracted rays are orthogonal at $i_p$.
    • Polarisation evidences transverse nature of light.
  • NEET Focus: YDSE formulae & fringe width, intensity expression, conditions for maxima/minima, single-slit minima & central width, Rayleigh criterion $1.22\lambda/D$, Malus’ & Brewster’s laws, coherence conditions.
Important Figures
Huygens construction for reflection and refraction
Huygens’ construction: deriving Snell’s law from secondary wavelets.
Young’s double slit geometry and fringe pattern
YDSE: $\beta=\lambda D/d$; maxima $\Delta=m\lambda$, minima $\Delta=(m+\tfrac12)\lambda$.
Single-slit diffraction and Rayleigh criterion for two point sources
Single-slit: central width $2\lambda/a$; Rayleigh: $\theta_{\min}=1.22\lambda/D$.
Quick Summary

Wave optics explains interference, diffraction, and polarisation. Master YDSE fringe width, intensity relations, single-slit minima and central width, resolution limits ($1.22\lambda/D$), and polarisation laws (Malus, Brewster) for rapid problem-solving.

Practice Quiz (10 MCQs)
1) Huygens’ principle states that:
2) In YDSE, the fringe width is:
3) Resultant intensity for equal source intensities $I_0$ with phase difference $\delta$ is:
4) Condition for destructive interference (path difference $\Delta$):
5) In single-slit diffraction, angular width of central maximum is approximately:
6) To improve the resolving power of a telescope, one should:
7) Malus’ law gives transmitted intensity through an analyser at angle $\theta$ (incident is plane-polarised with $I_0$):
8) Brewster’s law (air to medium of refractive index $n$) is:
9) For sustained interference, the two sources must be:
10) If slit width $a$ is decreased in a single-slit setup (same $\lambda$), then:
Downloads
Wave Optics — Formula & Facts (PDF) YDSE & Diffraction Diagrams (PNG) Polarisation: Malus & Brewster (PDF)
Cross-links

Continue with: Ray Optics & Optical Instruments · Dual Nature of Radiation & Matter

11 ATOMS

Modern Physics Weightage: Medium–High Updated: 10 Sep 2025
Chapter Notes
  • Early evidence & spectra: Electrons (J. J. Thomson, 1897); line spectra imply quantised internal atomic structure.
  • Rutherford scattering:
    • Most $\alpha$ pass undeviated; few large-angle deflections $\Rightarrow$ small, massive, positively charged nucleus.
    • Atomic size $\sim 10^{-10}\,\mathrm{m}$; nuclear size $\sim 10^{-15}$–$10^{-14}\,\mathrm{m}$ ($\sim 10^5$ times smaller).
    • Classical problem: radiating electrons should spiral into nucleus (instability) — not observed.
  • Bohr model (hydrogenic atoms):
    • Stationary (non-radiating) orbits; angular momentum quantised: $mvr=n\hbar$.
    • Orbit radius: $r_n=\dfrac{n^2 a_0}{Z}$, with $a_0=0.529\,\text{\AA}$; for H ($Z=1$): $r_n=n^2 a_0$.
    • Energy levels: $E_n=-\dfrac{13.6\,Z^2}{n^2}\ \text{eV}$; ionisation energy of H (from $n=1$) is $13.6\,\text{eV}$.
    • Transition $n_2\!\to\! n_1$ emits photon: $h\nu=E_{n_2}-E_{n_1}$; Rydberg form: $\dfrac{1}{\lambda}=R_H\!\left(\dfrac{1}{n_1^2}-\dfrac{1}{n_2^2}\right)$.
    • Series: Lyman ($n_1=1$, UV), Balmer ($n_1=2$, visible), Paschen ($n_1=3$, IR), etc.
  • de Broglie explanation of Bohr: Standing-wave condition $2\pi r_n=n\lambda$ with $\lambda=h/p$ gives $mvr=n\hbar$.
  • Limitations: Works well only for single-electron systems; cannot predict intensities/fine structure; incompatible with uncertainty principle — superseded by QM.
  • NEET Focus: $r_n, E_n$ formulae, ionisation energy, Rydberg relation & series, Rutherford conclusions, de Broglie standing-wave condition, orders of magnitude for atomic vs nuclear size.
Important Figures
Alpha-particle scattering off a thin foil
Rutherford $\alpha$-scattering: most pass straight; rare large-angle deflections ⇒ compact positive nucleus.
Quantised Bohr energy levels with labeled series
Bohr levels with Lyman, Balmer, Paschen series; $E_n=-13.6\,\mathrm{eV}/n^2$ (H).
Standing electron wave along circular orbit
de Broglie standing-wave condition $2\pi r_n=n\lambda$ gives $mvr=n\hbar$.
Quick Summary

Alpha scattering establishes the nucleus; Bohr’s quantised orbits explain hydrogen spectra: $r_n=\tfrac{n^2 a_0}{Z}$, $E_n=-\tfrac{13.6 Z^2}{n^2}$ eV, and $1/\lambda=R_H(1/n_1^2-1/n_2^2)$. de Broglie waves justify $mvr=n\hbar$. Know series (Lyman/Balmer) and ionisation energy (13.6 eV for H).

Practice Quiz (10 MCQs)
1) Rutherford’s $\alpha$-scattering showed that:
2) For hydrogen ($Z=1$), the Bohr orbit radius is:
3) The energy of the $n$th level in hydrogen is:
4) The wavelength of a photon emitted in transition $n_2\!\to\! n_1$ (H) obeys:
5) Ionisation energy of hydrogen from the ground state equals:
6) de Broglie’s standing-wave condition for a stable Bohr orbit is:
7) The Balmer series corresponds to transitions ending at:
8) A key limitation of the Bohr model is that it:
9) Order-of-magnitude ratio (atomic radius)/(nuclear radius) is about:
10) For a hydrogenic ion with atomic number $Z$, the energy level is:
Downloads
Atoms — Formula & Series Sheet (PDF) Bohr Levels & Transitions Diagram (PNG) Rutherford Scattering Quick Notes (PDF)
Cross-links

Continue with: Wave Optics · Nuclei

12 Nuclei

Modern Physics Weightage: High Updated: 10 Sep 2025
Chapter Notes
  • Nuclear basics: Nucleus is tiny, dense, positively charged; almost all atomic mass is nuclear. Atomic radius $\sim 10^{-10}\,\mathrm{m}$, nuclear radius $\sim 10^{-15}$–$10^{-14}\,\mathrm{m}$.
  • Mass units & composition:
    • $1\,\mathrm{u}= \dfrac{1}{12}m(^{12}\mathrm{C}) = 1.660539\times10^{-27}\,\mathrm{kg}$, and $1\,\mathrm{u}\,c^2 \approx 931.5\,\mathrm{MeV}$.
    • Nuclide notation ${}^A_Z\!X$; $A=Z+N$. Isotopes (same $Z$), isobars (same $A$), isotones (same $N$).
  • Nuclear size: Electron/scattering data $\Rightarrow\ R=R_0A^{1/3}$ with $R_0\approx 1.2\,\mathrm{fm}$. Nearly constant nuclear density $\rho\sim 2\!\times\!10^{17}\,\mathrm{kg\,m^{-3}}$.
  • Mass–energy & binding:
    • Mass defect $\Delta m = Zm_p+Nm_n - m_\text{nucleus}$.
    • Binding energy $E_b=\Delta m\,c^2$; per nucleon $E_{bn}=E_b/A$ gauges stability.
    • $E_{bn}$ peaks ($\sim 8.7$–$8.8\,\mathrm{MeV}$) for medium $A$ (Fe–Ni region) → energy via fusion (light nuclei) and fission (heavy nuclei).
  • Nuclear force: Strong, short-range ($\sim$ few fm), saturating, largely charge-independent (nn, pn, pp similar when Coulomb ignored).
  • Radioactivity:
    • Spontaneous decay: $\alpha$ (${}^4_2\mathrm{He}$), $\beta^\pm$ (electron/positron with $\bar\nu/\nu$), $\gamma$ (photon).
    • Decay law $N(t)=N_0e^{-\lambda t}$; half-life $T_{1/2}=\dfrac{\ln 2}{\lambda}$; activity $A=\lambda N$.
    • In $\beta^-$: $Z\!\to\! Z+1$ (A same); in $\beta^+$: $Z\!\to\! Z-1$ (A same); in $\alpha$: $A\!\to\!A-4$, $Z\!\to\!Z-2$.
  • Nuclear energy:
    • Fission (e.g., ${}^{235}\mathrm{U}$) of heavy nuclei releases energy; chain reaction needs critical mass, moderators, control rods.
    • Fusion (e.g., $4\,{}^1\mathrm{H}\to {}^4\mathrm{He}$) releases large energy; requires high $T$ and confinement (thermonuclear/plasma).
    • $Q$-value: $Q = \left(\sum m_\text{initial} - \sum m_\text{final}\right)c^2$ ($Q>0$ exoergic).
  • NEET Focus: $R=R_0A^{1/3}$, $1\,\mathrm{u}\,c^2\!=\!931.5$ MeV, mass defect $\to E_b$, $E_{bn}$ curve & implications, decay law & $T_{1/2}$, $\alpha/\beta/\gamma$ bookkeeping, basic fission vs fusion.
Important Figures
Nuclear radius scaling with A to the one-third
Nuclear size: $R=R_0A^{1/3}$ implies nearly constant nuclear density.
Binding energy per nucleon versus mass number curve
$E_{bn}$ vs $A$: peak near Fe–Ni; why fission (heavy) and fusion (light) release energy.
Exponential decay and half-life illustration
Radioactive decay: $N(t)=N_0e^{-\lambda t}$; $T_{1/2}=\ln2/\lambda$.
Quick Summary

Nuclei have radius $R\!=\!R_0A^{1/3}$ and near-constant density. Mass defect $\Delta m$ gives binding $E_b=\Delta mc^2$; per nucleon binding peaks for medium $A$, enabling energy from fusion (light) and fission (heavy). Radioactivity follows $N=N_0e^{-\lambda t}$ with $T_{1/2}=\ln2/\lambda$; track $Z,A$ changes for $\alpha,\beta,\gamma$ processes.

Practice Quiz (10 MCQs)
1) The nuclear radius scales approximately as:
2) The energy equivalent of $1\,\mathrm{u}$ is closest to:
3) Binding energy of a nucleus is defined as:
4) Which statement about the nuclear force is false?
5) In $\beta^-$ decay (electron emission), the changes in $(A,Z)$ are:
6) The radioactive decay law is $N(t)=N_0e^{-\lambda t}$. The half-life is:
7) The binding energy per nucleon is highest for medium-mass nuclei. This implies that:
8) For the reaction $X \rightarrow Y + \text{products}$, the $Q$-value is:
9) Which set correctly matches decay with typical emission?
10) The nearly constant nuclear density follows because:
Downloads
Nuclei — Formula & Concepts Sheet (PDF) Binding Energy per Nucleon Curve (PNG) Decay Law & Half-life Practice (PDF)
Cross-links

Continue with: Atoms · Semiconductor Electronics

13 Semiconductor Electronics: Materials, Devices & Simple Circuits

Electronics Weightage: High Updated: 10 Sep 2025
Chapter Notes
  • Material classes (by $\rho$/$\sigma$): Metals (very low $\rho$), semiconductors (intermediate), insulators (very high $\rho$). Elemental: Si, Ge; compound: GaAs, CdS.
  • Band picture: Valence band (VB), conduction band (CB), energy gap $E_g$.
    • Metals: partially filled CB / overlapping bands ($E_g\!\approx\!0$).
    • Insulators: large $E_g\!>\!3$ eV (e.g., diamond $\sim 5.4$ eV).
    • Semiconductors: small $E_g$ ($\mathrm{Si}\!\approx\!1.1$ eV, $\mathrm{Ge}\!\approx\!0.7$ eV).
  • Intrinsic semiconductor: Pure Si/Ge. At $T\!>\!0$, thermal breaking of covalent bonds $\Rightarrow$ free electron $e^-$ in CB + hole $h^+$ in VB; $n_e=n_h=n_i$; total current $I=I_e+I_h$; continual generation–recombination.
  • Doping (extrinsic):
    • n-type (donor: P, As, Sb): majority carriers $e^-$, minority $h^+$; donor level $E_D$ just below $E_C$.
    • p-type (acceptor: B, Al, In): majority $h^+$, minority $e^-$; acceptor level $E_A$ just above $E_V$.
    • Mass action law: $n_e n_h = n_i^2$ (at a given $T$). Crystal remains overall neutral.
  • $p$–$n$ junction: Diffusion $\Rightarrow$ depletion region (fixed ions), built-in barrier and electric field. At equilibrium: diffusion current = drift current; net current $=0$.
  • Biasing & diode I–V:
    • Forward bias ($p$ positive wrt $n$): barrier $\downarrow$, depletion width $\downarrow$, large current after threshold ($\sim\!0.7$ V Si, $\sim\!0.2$ V Ge).
    • Reverse bias: barrier $\uparrow$, tiny nearly-constant minority (saturation) current until breakdown.
    • Small-signal (dynamic) resistance: $r_d=\dfrac{\Delta V}{\Delta I}$.
  • Rectifiers & filters: Half-wave (1 diode) → pulsating DC at $f$; full-wave (2-diode CT or bridge) → ripple at $2f$. Smoothing with capacitive/inductive filters reduces ripple.
  • NEET Focus: $E_g$ trends; $n$- vs $p$-type (dopants & carriers); $n_e n_h=n_i^2$; depletion region & barrier; forward vs reverse bias characteristics; rectifier outputs & ripple frequency; meaning of dynamic resistance.
Important Figures
Valence band, conduction band and bandgap diagrams for metal, semiconductor and insulator
Energy bands: metal (overlap), semiconductor (small $E_g$), insulator (large $E_g$).
PN junction depletion region and built-in electric field
$p$–$n$ junction formation: depletion region with fixed charges & built-in field.
Half-wave and full-wave rectifier waveforms with ripple
Half-wave vs full-wave rectification; ripple frequency $f$ vs $2f$.
Quick Summary

Semiconductors have small $E_g$ so thermal/doping control of carriers is possible. Donors (P/As/Sb) yield $n$-type (majority $e^-$); acceptors (B/Al/In) yield $p$-type (majority $h^+$); $n_e n_h=n_i^2$. A $p$–$n$ junction forms a depletion region and barrier; forward bias lowers the barrier (large current), reverse bias yields small saturation current until breakdown. Rectifiers turn AC into pulsating DC; filters smooth the output.

Practice Quiz (10 MCQs)
1) In an intrinsic semiconductor at temperature $T>0$:
2) Doping Si with P (phosphorus) produces:
3) At $0\,\mathrm{K}$, an intrinsic semiconductor behaves as a/an:
4) The donor level $E_D$ in an $n$-type semiconductor lies:
5) Forward biasing a $p$–$n$ junction primarily:
6) Under reverse bias (below breakdown), the diode current is mainly due to:
7) A full-wave rectifier fed with $50\,\mathrm{Hz}$ AC has ripple (output) frequency:
8) For an extrinsic semiconductor at fixed $T$:
9) The small-signal (dynamic) resistance of a diode is defined as:
10) Which statement is correct at room temperature?
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Semiconductors — Key Formulae & I–V Traits (PDF) PN Junction & Biasing Diagrams (PNG) Rectifiers & Filters Quick Sheet (PDF)
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