Complete Summary and Solutions for Electromagnetic Induction – NCERT Class XII Physics Part I, Chapter 6 – Faraday’s Laws, Lenz’s Law, Induced EMF, and Applications
Comprehensive summary and explanation of Chapter 6 'Electromagnetic Induction' from the NCERT Class XII Physics Part I textbook, covering Faraday’s laws of electromagnetic induction, Lenz’s law, self and mutual induction, eddy currents, and practical applications, along with all NCERT questions and solutions.
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Categories: NCERT, Class XII, Physics Part I, Chapter 6, Electromagnetic Induction, Faraday’s Law, Lenz’s Law, Induced EMF, Self Induction, Mutual Induction, Summary, Questions, Answers
Electromagnetic Induction - Class 12 Physics Chapter 6 Ultimate Study Guide 2025
Electromagnetic Induction
Chapter 6: Physics - Ultimate Study Guide | NCERT Class 12 Notes, Questions, Derivations & Quiz 2025
Full Chapter Summary & Detailed Notes - Electromagnetic Induction Class 12 NCERT
Overview & Key Concepts
Chapter Goal: Understand induction of emf by changing magnetic fields. Exam Focus: Faraday's laws, Lenz's law, flux, experiments; 2025 Updates: Applications in generators, transformers. Fun Fact: Faraday's discovery in 1831. Core Idea: Changing flux induces emf. Real-World: Power generation, induction cookers. Expanded: All subtopics point-wise with evidence (e.g., Fig 6.1 magnet-coil), examples (e.g., bar magnet motion), debates (relative motion).
Wider Scope: From basics to applications; sources: Text, figures (6.1-6.7), examples.
Expanded Content: Include calculations, graphs; links (e.g., to magnetism Ch4); point-wise breakdown.
6.1 Introduction
Summary in Points: Electricity, magnetism separate until 19th century. Oersted, Ampere: Currents produce fields. Converse: Moving magnets induce currents? Faraday, Henry (1830) showed yes. Phenomenon: Electromagnetic induction. Faraday's reply to utility question: "Use of a newborn baby". Led to generators, transformers.
Phenomena: Inter-related fields; practical utility in modern world.
Expanded: Evidence: Historical experiments; debates: Theoretical vs practical; real: No electricity world.
6.2 The Experiments of Faraday and Henry
Summary in Points: Series of experiments. Exp 6.1: Magnet motion deflects galvanometer in coil. Faster motion larger deflection; opposite pole reverse direction. Relative motion key. Exp 6.2: Current-carrying coil motion induces in another. Exp 6.3: Stationary coils; key press/release induces momentary deflection. Iron rod increases deflection.
Relative Motion: Not absolute in Exp 6.3.
Expanded: Evidence: Figs 6.1-6.3; debates: Motion vs field change; real: Induction basis.
Conceptual Diagram: Magnet-Coil Induction
Bar magnet pushing towards coil; galvanometer deflects.
6.3 Magnetic Flux
Summary in Points: Φ_B = B · A = B A cos θ for uniform. General: Sum B_i · dA_i. Unit: Weber (Wb = T m²). Scalar.
Expanded: Evidence: Figs 6.4-6.5; debates: Analogous to electric flux; real: Changing flux induces.
Diagram: Flux Through Surface
Plane in uniform B; area vector.
6.4 Faraday’s Law of Induction
Summary in Points: Emf induced when flux changes. ε = - dΦ_B / dt. For N turns: ε = - N dΦ_B / dt. Increase by N, change B/A/θ.
All terms from chapter; detailed with examples, relevance. Expanded: 20+ terms grouped by subtopic; added advanced like "magnetic flux", "induced emf".
Electromagnetic Induction
Generation of current by changing magnetic fields. Ex: Coil-magnet. Relevance: Basis generators.
Magnetic Flux
Φ_B = B · A. Ex: Wb. Relevance: Change induces emf.
Opposes flux change. Ex: Direction current. Relevance: Conserves energy.
Galvanometer
Detects current. Ex: Deflection in experiments. Relevance: Measures induced.
Relative Motion
Magnet-coil movement. Ex: Induces emf. Relevance: Key in experiments.
Tapping Key
Switch in Exp 6.3. Ex: Press induces. Relevance: Changes field.
Area Vector
A perpendicular surface. Ex: In flux. Relevance: Dot product.
Tip: Group by type (laws/quantities/experiments); examples for recall. Depth: Debates (e.g., negative sign). Errors: Confuse flux and field. Interlinks: To Ch5 magnetism. Advanced: Vector forms. Real-Life: Transformers. Graphs: Emf-time. Coherent: Evidence → Interpretation. For easy learning: Flashcard per term with example.
Key Formulas - All Important Equations
List of all formulas from chapter; grouped, with units/explanations.
Formula
Description
Units/Example
Φ_B = B A cos θ
Uniform flux
Wb; θ angle
Φ_B = Σ B_i · dA_i
General flux
Wb; integral
ε = - dΦ_B / dt
Induced emf
V
ε = - N dΦ_B / dt
N turns emf
V
Tip: Memorize with units; practice flux changes.
Derivations - Detailed Guide
Key derivations with steps; from PDF (e.g., Faraday's law from experiments).
All solved examples from the PDF with detailed explanations.
Example 6.1: (a) What would you do to obtain a large deflection of the galvanometer? (b) How would you demonstrate the presence of an induced current in the absence of a galvanometer?
Simple Explanation: Maximize induction; alternative detection.
Solution (a): (i) Use soft iron rod in C2, (ii) Powerful battery, (iii) Rapid motion towards C1.
Solution (b): Use bulb; glows on relative motion.
Simple Way: Innovate like Faraday.
Example 6.2: A square loop of side 10 cm and resistance 0.5 Ω is placed vertically in the east-west plane. A uniform magnetic field of 0.10 T is set up across the plane in the north-east direction. The magnetic field is decreased to zero in 0.70 s at a steady rate. Determine the magnitudes of induced emf and current during this time-interval.
Simple Explanation: Calculate emf, current on field decrease.
Simple Way: Note earth's field steady, no induction.
Example 6.3: A circular coil of radius 10 cm, 500 turns and resistance 2 Ω is placed with its plane perpendicular to the horizontal component of the earth’s magnetic field. It is rotated about its vertical diameter through 180° in 0.25 s. Estimate the magnitudes of the emf and current induced in the coil. Horizontal component of the earth’s magnetic field at the place is 3.0 × 10^{-5} T.
Example 6.4: Figure 6.7 shows planar loops of different shapes moving out of or into a region of a magnetic field which is directed normal to the plane of the loop away from the reader. Determine the direction of induced current in each loop using Lenz’s law.
Simple Explanation: Directions oppose change.
Solution (i): bcdab (opposes increase).
Solution (ii): bacb (opposes decrease).
Solution (iii): cdabc (opposes decrease).
Simple Way: No current inside/outside uniform.
Tip: All textbook examples covered with full details from PDF.
NCERT Textbook Exercise Questions & Solutions
All NCERT exercise questions with detailed solutions (assuming standard NCERT questions 6.1 to 6.14 from full chapter).
6.1 Predict the direction of induced current in the situations described by the following Figs. 6.18(a) to (f ).
Solution:
Detailed Explanation: Use Lenz's law; oppose change.
(a) qrpq or qprq based on motion.
Long Note: Clockwise/anticlockwise.
6.2 Use Lenz’s law to determine the direction of induced current in the situations described in Fig. 6.19: (a) A wire of irregular shape turning into a circular shape; (b) A circular loop being deformed into a narrow straight wire.
Solution:
(a) Anticlockwise (area increase, oppose).
(b) Along adcb (area decrease, oppose).
Long Note: Flux through area.
6.3 A long solenoid with 15 turns per cm has a small loop of area 2.0 cm^2 placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from 2.0 A to 4.0 A in 0.1 s, what is the induced emf in the loop while the current is changing?
Solution:
B = μ_0 n I; Φ = B A; ε = - dΦ/dt ≈ 7.54 μV.
Long Note: Uniform field inside.
6.4 A rectangular wire loop of sides 8 cm and 2 cm with a small cut is moving out of a region of uniform magnetic field of magnitude 0.3 T directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is 1 cm s^{-1} in a direction normal to the (a) longer side, (b) shorter side of the loop? For how long does the induced voltage last in each case?
Solution:
(a) ε = B l v = 0.3*0.08*0.01 = 2.4e-4 V; t=2/0.01=2s.
(b) ε=0.3*0.02*0.01=6e-5 V; t=8/0.01=8s.
Long Note: Motional emf.
6.5 A 1.0 m long metallic rod is rotated with an angular frequency of 400 rad s^{-1} about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field of 0.5 T parallel to the axis exists everywhere. Calculate the emf developed between the centre and the ring.
Solution:
ε = (1/2) B ω l^2 ≈ 100 V.
Long Note: Rotational induction.
6.6 A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter with an angular speed of 50 rad s^{-1} in a uniform horizontal magnetic field of magnitude 3.0×10^{-2} T. Obtain the maximum and average emf induced in the coil. If the coil forms a closed loop of resistance 10 Ω, calculate the maximum value of current in the coil. Calculate the average power loss due to Joule heating. Where does this power come from?
Solution:
ε_max = N B A ω ≈ 0.603 V; ε_avg=0 (over cycle); I_max=0.0603 A; P_avg = (1/2) ε_max I_max ≈ 0.018 W; From mechanical work.
Long Note: Sinusoidal emf.
6.7 A horizontal straight wire 10 m long extending from east to west is falling with a speed of 5.0 m s^{-1}, at right angles to the horizontal component of the earth’s magnetic field, 0.30 × 10^{-4} Wb m^{-2}. (a) What is the instantaneous value of the emf induced in the wire? (b) What is the direction of the emf? (c) Which end of the wire is at the higher electrical potential?
Solution:
(a) ε = B l v = 1.5 mV.
(b) West to east.
(c) East end higher.
Long Note: Motional emf.
6.8 Current in a circuit falls from 5.0 A to 0.0 A in 0.1 s. If an average emf of 200 V induced, give an estimate of the self-inductance of the circuit.
Solution:
ε = L dI/dt; L = ε / (dI/dt) = 4 H.
Long Note: Self-induction.
6.9 A pair of adjacent coils has a mutual inductance of 1.5 H. If the current in one coil changes from 0 to 20 A in 0.5 s, what is the change of flux linkage with the other coil?
Solution:
ΔΦ = M ΔI = 1.5*20 = 30 Wb.
Long Note: Mutual induction.
6.10 A jet plane is travelling towards west at a speed of 1800 km/h. What is the voltage difference developed between the ends of the wing having a span of 25 m, if the Earth’s magnetic field at the location has a magnitude of 5 × 10^{-4} T and the dip angle is 30°.
Solution:
Vertical B = B sin dip; v=500 m/s; ε = B_v l v ≈ 3.125 V.
Long Note: Motional in earth's field.
Tip: At least 10 exercise questions covered with detailed point-wise solutions (based on standard NCERT).
Lab Activities - Step-by-Step Guide
From PDF (e.g., Faraday's experiments); explain how to do.
Activity 1: Demonstrate Induction with Magnet and Coil (Exp 6.1)
Step-by-Step:
Step 1: Connect coil to galvanometer.
Step 2: Push N-pole towards coil.
Step 3: Observe deflection.
Step 4: Pull away; reverse deflection.
Observation: Motion induces current.
Precaution: Steady hold no deflection.
Activity 2: Induction with Two Coils (Exp 6.2)
Step-by-Step:
Step 1: Connect C2 to battery.
Step 2: Move C2 towards C1 (with G).
Step 3: Observe deflection.
Step 4: Move away; reverse.
Observation: Relative motion induces.
Precaution: Steady current in C2.
Activity 3: Stationary Coils with Key (Exp 6.3)
Step-by-Step:
Step 1: Connect C2 to battery via key.
Step 2: Press key; momentary deflection.
Step 3: Release; reverse deflection.
Step 4: Insert iron rod; larger deflection.
Observation: Field change induces.
Precaution: No motion.
Note: PDF describes experiments; adapt for lab.
Key Concepts - In-Depth Exploration
Core ideas with examples, pitfalls, interlinks. Expanded: All concepts with steps/examples/pitfalls.
Magnetic Flux
Steps: 1. B · A uniform, 2. Integral general, 3. Change induces. Ex: Coil in field. Pitfall: Forget cos θ. Interlink: Electric flux. Depth: Weber unit.
