Chapter 2 of 14

14%

ICSE Class 12 Physics★ Full ISC Class 12 Physics syllabus · 70 marks theory + 30 marks practical · Board: ISC

Physics — Electricity, Magnetism, Optics & Modern Physics

ISC Class 12 Physics: ELECTROSTATICS and CURRENT ELECTRICITY. MAGNETIC effects and ELECTROMAGNETIC INDUCTION. ALTERNATING CURRENT. OPTICS — reflection, refraction, wave optics. DUAL NATURE of radiation and matter. ATOMS and NUCLEI. SEMICONDUCTORS. ISC Class 12 Physics.

⏱ 22 min readHard difficulty✓ Free · NCERT-aligned

Worksheet

Podcast

Listen as a conversation

A teacher & a student talk through the chapter — in your language.

Mind Map

The chapter at a glance

Every concept and exam-favourite branch — revisable in 5 minutes.

…

Study Guide

Night-before notes

Key points, glossary and the questions most likely to show up.

…

VocabularyBuild your vocabularyLexiGenome mines the key words and schedules them with spaced repetition.Mine words →

By the end of this chapter you'll be able to…

1Apply Gauss's law to calculate electric fields for symmetric charge distributions; use capacitance and energy equations for series/parallel combinations
2Solve Kirchhoff's law circuits; calculate resistance using Wheatstone bridge and potentiometer; apply Nernst-style reasoning to EMF vs terminal voltage
3Derive and apply Faraday's laws, Lenz's law, transformer equations, and LCR series circuit equations including resonance condition and power factor
4Solve ray optics problems (mirror and lens formulae, refraction, TIR, prism) and wave optics problems (Young's double slit fringe width, diffraction condition)
5Apply photoelectric effect equations (Einstein, threshold frequency, stopping potential), Bohr's model energy levels, and radioactive decay law to solve problems

💡

Why this chapter matters

ISC Physics covers all of modern physics in one paper — electrostatics through semiconductor electronics. The paper has a balanced mix of derivations, numerical problems, and conceptual questions. Electromagnetic induction (Faraday's laws, transformer equations), alternating current (LCR resonance, power factor), and wave optics (Young's double slit, diffraction) are derivation-intensive and almost certainly appear. Photoelectric effect and Bohr's model are standard 4-6 mark questions. Semiconductors (diode, transistor as amplifier) conclude the syllabus.

Before you start — revise these

A 5-minute refresher here will save you 30 minutes of confusion below.

🔗

Physics — Electromagnetism, Optics & Modern Physics

1. Electrostatics

Coulomb's Law: F = kq₁q₂/r². k = 1/(4πε₀) = 9×10⁹ Nm²/C².

Electric Field: E = F/q. E = kq/r² (point charge). Gauss's Law: Φ = ∮E·dA = q_enclosed/ε₀.

Electric Potential: V = kq/r. ΔV = −∫E·dr. Capacitance C = Q/V. Energy stored = ½CV² = Q²/(2C). Capacitors in series: 1/C = Σ1/Cᵢ. Parallel: C = ΣCᵢ.

2. Current Electricity

Ohm's Law: V = IR. Resistivity ρ: R = ρL/A. Temperature: R_t = R₀(1+αΔT).

Kirchhoff's Laws

KCL (Junction) : ΣI_in = ΣI_out. KVL (Loop) : ΣΔV around a closed loop = 0.

Wheatstone Bridge — Balanced: R₁/R₂ = R₃/R₄. Metre Bridge — finds unknown resistance.

Potentiometer — Compares EMFs. Measures internal resistance. 'No current draw = TRUE EMF.'

3. Magnetic Effects of Current

Biot-Savart Law: dB = (μ₀/4π)(Idl sin θ/r²). Direction: Right-hand rule.

Straight Wire: B = μ₀I/(2πr). Circular Loop (centre) : B = μ₀I/(2R). Solenoid: B = μ₀nI (interior).

Force on Moving Charge: F = q(v × B). Lorentz Force = q(E + v × B).

Cyclotron — Accelerates charged particles.

Force Between Parallel Currents: I in SAME direction → ATTRACT. Opposite → REPEL.

Ampere's Circuital Law: ∮B·dl = μ₀I_enclosed.

4. Moving Coil Galvanometer — Converts to Ammeter (low shunt R) and Voltmeter (high series R).

5. Electromagnetic Induction

Faraday's Laws

Induced EMF: ε = −dΦ_B/dt. Lenz's Law: Induced current OPPOSES the change in flux.

Motional EMF: ε = Blv (conductor moving in perpendicular B).

Self-Inductance L: ε = −L dI/dt. Mutual Inductance M: ε₁ = −M dI₂/dt.

Transformer: Vₚ/Vₛ = Nₚ/Nₛ. Step-up (Nₛ>Nₚ). Step-down (Nₛ<Nₚ). 'Power conserved (ideal): VₚIₚ = VₛIₛ.' Eddy currents — reduced by LAMINATION.

6. Alternating Current (AC)

Instantaneous: V(t) = V₀ sin ωt. I(t) = I₀ sin ωt.

RMS Values: V_rms = V₀/√2. I_rms = I₀/√2.

Reactance and Impedance

Resistor R: V and I in PHASE. Inductor X_L = ωL: V LEADS I by 90°. Capacitor X_C = 1/(ωC): V LAGS I by 90°.
Series LCR: Z = √[R² + (X_L − X_C)²].

Resonance: ω₀ = 1/√(LC). Z is MINIMUM (=R). Current MAXIMUM. 'Tuning a radio uses LCR resonance.'

Power in AC: P_avg = V_rms I_rms cos φ. cos φ = power factor.

7. Electromagnetic Waves

Maxwell predicted: changing E → B. Changing B → E. EM waves are SELF-PROPAGATING. Speed c = 1/√(μ₀ε₀) = 3×10⁸ m/s. Transverse. Spectrum: Radio → Microwave → IR → Visible → UV → X-ray → Gamma.

8. Optics — Ray Optics

Reflection: Laws. Mirror formula: 1/f = 1/u + 1/v. m = −v/u.

Refraction: Snell's Law: n₁ sin i = n₂ sin r. n = c/v.

Total Internal Reflection (TIR) — when i > i_c. i_c = sin⁻¹(1/n). Optical fibres.

Lenses — Lens formula: 1/f = 1/v − 1/u. Lens maker's formula: 1/f = (n−1)(1/R₁ − 1/R₂).

Prism: δ = (μ−1)A. Minimum deviation: δ_m. Dispersive power: ω = (μ_V−μ_R)/(μ_Y−1).

9. Wave Optics

Huygens' Principle. Interference. Young's Double Slit: Fringe width β = λD/d.

Diffraction — Single slit: Angular width = 2λ/a.

Polarisation — Proves light is TRANSVERSE. Brewster's Law: tan θ_p = n.

10. Dual Nature of Radiation and Matter

Photoelectric Effect: Einstein: E = hf. K_max = hf − φ (φ = work function). Threshold frequency f₀ = φ/h.
De Broglie Wavelength: λ = h/p = h/(mv).

11. Atoms and Nuclei

Bohr's Model: E_n = −13.6/n² eV. Spectral series: Lyman (UV). Balmer (visible). Paschen (IR). 'Energy LEVELS are quantised — electrons can only occupy DISCRETE orbits.'

Nucleus

Radius: R = R₀A^(1/3). Mass Defect: Δm = [Zmₚ + (A−Z)mₙ] − M_nucleus. Binding Energy = Δm·c².
Radioactive Decay: N(t) = N₀e^(−λt). Half-life T₁/₂ = ln2/λ.

Nuclear Fission and Fusion

12. Semiconductor Electronics

Diode — PN Junction: Forward bias → conducts. Reverse bias → blocks. Rectifier.

Transistor — NPN/PNP. Amplifier (CE configuration). Voltage gain A_V = −βR_C/R_in.

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Electrostatics and Current Electricity — Core Equations

Coulomb: F = kq₁q₂/r². k = 9×10⁹ Nm²/C². Gauss: Φ = q_enc/ε₀. Capacitors: Series: 1/C = Σ1/Cᵢ. Parallel: C = ΣCᵢ. Energy: U = ½CV² = Q²/2C = QV/2. Ohm: V = IR. Resistivity: R = ρL/A. R_T = R₀(1+αΔT). Kirchhoff: KCL: ΣI = 0 at junction. KVL: ΣV = 0 around loop. Wheatstone bridge balanced: R₁/R₂ = R₃/R₄.

Potentiometer principle: potential drop ∝ length. For unknown EMF: E₂/E₁ = l₂/l₁. For internal resistance: r = R(l₁−l₂)/l₂ where l₁ = balancing length without R, l₂ = with R. Potentiometer is preferred over voltmeter because it draws NO current from the cell — measures TRUE EMF.

Electromagnetic Induction and AC Circuits

Faraday: ε = −dΦ/dt = −N·dΦ/dt (for N-turn coil). Lenz's law: induced current OPPOSES change in flux. Motional EMF: ε = BLv. Self-inductance: ε = −L(dI/dt). Mutual inductance: ε₂ = −M(dI₁/dt). Transformer: Vₛ/Vₚ = Nₛ/Nₚ = Iₚ/Iₛ. AC: Xₗ = ωL. Xc = 1/(ωC). Z = √[R² + (Xₗ−Xc)²]. Resonance: ω₀ = 1/√(LC). Quality factor Q = ω₀L/R. Power: P = V_rms·I_rms·cosφ. Power factor cosφ = R/Z.

V_rms = V₀/√2. I_rms = I₀/√2. At RESONANCE: Z = R (minimum), I = maximum, cosφ = 1, power = maximum. LC circuit oscillates with ω = 1/√(LC) — frequency same as AC resonance.

Optics — Ray and Wave

MIRRORS: 1/f = 1/v + 1/u. m = −v/u. Sign convention: distances measured from POLE; incident ray direction POSITIVE. LENSES: 1/f = 1/v − 1/u. m = v/u. Lens maker's: 1/f = (n−1)(1/R₁−1/R₂). SNELL: n₁sinθ₁ = n₂sinθ₂. TIR: sinθc = 1/n (denser to rarer). PRISM: δ_min when r₁=r₂=A/2; n = sin[(A+δm)/2]/sin(A/2). YOUNG'S DSE: β (fringe width) = λD/d. Path diff for bright: nλ. Dark: (2n−1)λ/2. SINGLE SLIT diffraction: first minima at sinθ = λ/a (a = slit width). BREWSTER: tanθ_B = n.

In ISC mirror problems: use NEW CARTESIAN sign convention throughout. All distances from the pole. Distances in direction of incident light are positive. For real object, u is always NEGATIVE (object is in front of mirror). Real image: v is negative (concave mirror, beyond C or F).

Modern Physics — Photoelectric Effect, Bohr, Nucleus

PHOTOELECTRIC EFFECT (Einstein): E = hf = hc/λ. KE_max = hf − φ (φ = work function = hf₀). Stopping potential V₀: eV₀ = KE_max. Threshold wavelength λ₀ = hc/φ. DE BROGLIE: λ = h/p = h/(mv) = h/√(2mKE). BOHR MODEL: E_n = −13.6/n² eV (hydrogen). r_n = n²a₀ = n² × 0.529 Å. v_n = 2.18×10⁶/n m/s. RADIOACTIVE DECAY: N = N₀e^(−λt). T₁/₂ = 0.693/λ. Activity A = λN. MASS DEFECT: Δm = [Zmₚ + Nmₙ − M_nucleus]. BE = Δm × c² = Δm × 931.5 MeV/amu.

KEY SPECTRAL SERIES: Lyman (n_f=1, UV). Balmer (n_f=2, visible). Paschen (n_f=3, near IR). Energy of photon emitted = E_higher − E_lower = 13.6(1/n₁² − 1/n₂²) eV. SEMICONDUCTOR: Diode: forward bias ≈0.7V (Si), reverse: depleted. Transistor in CE: A_V = −βR_C/R_in. β = I_C/I_B.

⚠️

Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Using the wrong sign convention in mirror and lens problems

✓ ISC uses the NEW CARTESIAN SIGN CONVENTION: All distances measured from the OPTICAL CENTRE/POLE. The direction of INCIDENT LIGHT is POSITIVE (typically left to right). Object is ALWAYS to the left of mirror/lens, so u = NEGATIVE. For a concave mirror: f = negative, R = negative. For a convex mirror: f = positive. For convex lens: f = positive. For concave lens: f = negative. Check: 1/f = 1/v − 1/u for lens; 1/f = 1/v + 1/u for mirror.

WATCH OUT

✗ Saying photocurrent increases with frequency (or that frequency affects current)

✓ INTENSITY determines photocurrent (more photons per second = more photoelectrons = more current). FREQUENCY determines the KINETIC ENERGY of emitted photoelectrons (higher frequency → more energy per photon → more KE_max). Frequency must exceed the THRESHOLD FREQUENCY to cause emission at all — but above threshold, KE increases linearly with frequency, not current.

WATCH OUT

✗ Confusing transformer voltage and current ratios

✓ For an IDEAL transformer: Vₛ/Vₚ = Nₛ/Nₚ (voltage ratio = turns ratio). CURRENT: Iₛ/Iₚ = Nₚ/Nₛ (inverse of turns ratio). Power is conserved: VₛIₛ = VₚIₚ. Step-UP transformer: Nₛ > Nₚ → higher voltage → LOWER current. Step-DOWN: Nₛ < Nₚ → lower voltage → HIGHER current. Power is transmitted at HIGH voltage (low current) to reduce I²R losses in transmission lines.

Practice problems

Try each one yourself before tapping "Show solution". Active recall > rereading.

Q1EASY· photoelectric-effect

Light of wavelength 400 nm falls on a metal with work function 2.0 eV. Find (a) the maximum kinetic energy of emitted electrons and (b) the stopping potential. (h = 6.63×10⁻³⁴ J·s, c = 3×10⁸ m/s, 1 eV = 1.6×10⁻¹⁹ J)

▶ Show solution

(a) Energy of photon: E = hc/λ = (6.63×10⁻³⁴ × 3×10⁸)/(400×10⁻⁹) = 4.97×10⁻¹⁹ J = 4.97×10⁻¹⁹/(1.6×10⁻¹⁹) = 3.1 eV. KE_max = E − φ = 3.1 − 2.0 = 1.1 eV. (b) Stopping potential V₀: eV₀ = KE_max = 1.1 eV → V₀ = 1.1 V.

Q2MEDIUM· optics-lens

A convex lens of focal length 20 cm forms a real image of an object placed 30 cm in front of it. Find the image distance, magnification, and state whether the image is erect or inverted.

▶ Show solution

Using sign convention: u = −30 cm (object to the left), f = +20 cm (convex lens). Lens formula: 1/v − 1/u = 1/f → 1/v − 1/(−30) = 1/20 → 1/v + 1/30 = 1/20 → 1/v = 1/20 − 1/30 = 3/60 − 2/60 = 1/60. v = +60 cm (real image, on the other side). Magnification m = v/u = 60/(−30) = −2. The image is REAL (v is positive), INVERTED (m is negative), and MAGNIFIED (|m| = 2).

Q3HARD· electromagnetic-induction

A rectangular coil of N=100 turns, area A=0.02 m², resistance R=20 Ω, rotates in a magnetic field B=0.5 T at ω=100π rad/s. Find (a) peak EMF, (b) rms EMF, (c) rms current, (d) average power dissipated.

▶ Show solution

(a) Peak EMF: ε₀ = NBAω = 100 × 0.5 × 0.02 × 100π = 100π ≈ 314.16 V. (b) rms EMF: ε_rms = ε₀/√2 = 100π/√2 = 100×3.14/1.414 ≈ 222 V. (c) rms current: I_rms = ε_rms/R = 222/20 = 11.1 A. (d) Average power: P = I_rms² × R = (11.1)² × 20 = 123.21 × 20 ≈ 2464 W ≈ 2.46 kW.

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•Gauss's law: Φ = q_enc/ε₀. For sphere: E = q/(4πε₀r²). For cylinder: E = λ/(2πε₀r).
•Wheatstone bridge balanced: R₁/R₂ = R₃/R₄. Potentiometer: no current drawn = true EMF.
•Faraday: ε = −dΦ/dt. Lenz: induced current opposes change in flux.
•Transformer: Vₛ/Vₚ = Nₛ/Nₚ. Power transmitted at HIGH voltage (low I²R loss).
•LCR resonance: ω₀ = 1/√(LC). Z_min = R. Power factor = 1 at resonance.
•Mirror: 1/f = 1/v + 1/u. Lens: 1/f = 1/v − 1/u. Both: m = −v/u (mirror), v/u (lens).
•Young's DSE: β = λD/d. Increasing D or λ increases fringe width. Increasing d decreases it.
•Photoelectric: KE_max = hf − φ. Intensity → current. Frequency → kinetic energy.
•Bohr: E_n = −13.6/n² eV. Hydrogen emission: E = 13.6(1/n₁² − 1/n₂²) eV.
•Radioactive decay: N = N₀e^(−λt). T₁/₂ = 0.693/λ. Activity A = λN.

ICSE marks blueprint

Where the marks come from in this chapter — so you can plan your prep.

Where this shows up in the real world

This chapter isn't just an exam topic — it lives in the world around you.

Going beyond the textbook

For olympiad aspirants and curious learners — topics that build on this chapter.

Research Maxwell's Equations — the four equations that unified electricity, magnetism, and light into a single framework (1865). They are: Gauss's Law for electricity, Gauss's Law for magnetism (no monopoles), Faraday's Law, and Ampere-Maxwell Law. Maxwell's prediction that light is an electromagnetic wave was confirmed by Hertz (1887). Investigate how these 4 equations underlie ALL classical electromagnetism.
Investigate Special Relativity (Einstein, 1905) — the speed of light is the same for all observers. Consequences: time dilation, length contraction, E=mc² (mass-energy equivalence). The Lorentz transformation replaces Galilean transformation. Research the twin paradox and how GPS satellites must use relativistic corrections to function.
Explore Quantum Mechanics beyond ISC — the Schrödinger equation, wave functions, the uncertainty principle (ΔxΔp ≥ ℏ/2), and quantum entanglement. The 2022 Nobel Prize in Physics was awarded for entanglement experiments. Research how quantum computers exploit these principles to solve problems classical computers cannot.
Research Superconductors — materials that conduct electricity with ZERO resistance below a critical temperature. High-temperature superconductors (1987, discovered in cuprate ceramics) work above liquid nitrogen temperature. Applications include MRI machines, particle accelerators, and potentially loss-free power transmission. Investigate the unsolved puzzle of high-Tc superconductivity.

Where else this chapter is tested

CBSE board isn't the only one — other exams test this chapter too.

AI helpers for this chapter

Generate more practice on the fly, or have the chapter explained at a different level.

⚡

Generate 5 more questions

Fresh MCQs + short-answer items based on this chapter, plus answer keys.

🧠

Explain at a different level

Re-explain the chapter at the level you actually want.

📝 My notes

Saved on this device — sign in to sync · how this works

0/600

Questions students ask

The real ones — pulled from the Q&A community and tutor sessions.

SELF-INDUCTANCE (L): The property of a coil to oppose changes in its OWN current. When current changes in a coil, the changing magnetic flux induces an EMF in the SAME coil: ε = −L(dI/dt). Unit: Henry (H). MUTUAL INDUCTANCE (M): The property of two coils whereby a changing current in coil 1 induces an EMF in coil 2: ε₂ = −M(dI₁/dt). M depends on the geometry of both coils and their relative position. The TRANSFORMER works on the principle of mutual inductance.

Power dissipated in transmission lines = I²R. For a given power P = VI, if voltage V is INCREASED (step-up transformer), current I = P/V DECREASES. Since power loss = I²R, a lower current means MUCH LESS heating loss in the cables. High-voltage transmission (400 kV in India's grid) reduces transmission losses enormously. At the destination, step-down transformers reduce the voltage to safe levels for domestic use (230 V in India).

Practice more, ask doubts, find a tutor

ICSE Class 12 mock tests

ICSE Class 12 PYQs

Ask in Q&A

Physics flashcards

Related chapters

Students who read Physics — Electricity, Magnetism, Optics & Modern Physics usually read these next.

'Electric Charges and Fields'

'Coulombs law, electric field and field lines, electric dipole, Gausss theorem and its applications to charged spheres, cylinders, and planes.'

'Electrostatic Potential and Capacitance'

'Electric potential, equipotential surfaces, capacitance, parallel plate capacitor, dielectrics, energy stored in a capacitor, and combinations of capacitors.'

'Current Electricity'

'Ohms law, resistivity, series and parallel circuits, EMF and internal resistance, Kirchhoffs laws, Wheatstone bridge, meter bridge, and potentiometer.'