Complete Summary and Solutions for Moving Charges and Magnetism – NCERT Class XII Physics Part I, Chapter 4 – Magnetic Field, Motion of Charged Particles, and Electromagnetic Effects
Detailed summary and explanation of Chapter 4 'Moving Charges and Magnetism' from the NCERT Class XII Physics Part I textbook, covering magnetic fields, force on a moving charge, motion of charged particles in magnetic and electric fields, magnetic force on a current-carrying conductor, Biot-Savart law, Ampere’s law, and applications, along with all NCERT questions and answers.
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Categories: NCERT, Class XII, Physics Part I, Chapter 4, Moving Charges, Magnetism, Magnetic Field, Force on Charge, Electromagnetic Effects, Summary, Questions, Answers
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Moving Charges and Magnetism
Chapter 4: Physics - Ultimate Study Guide | NCERT Class 12 Notes, Questions, Derivations & Quiz 2025
Full Chapter Summary & Detailed Notes - Moving Charges and Magnetism Class 12 NCERT
Overview & Key Concepts
- Chapter Goal: Understand magnetic fields due to moving charges, forces on charges in fields, applications like cyclotron. Exam Focus: Definitions, formulas, derivations for Lorentz force, Biot-Savart law; 2025 Updates: Real-life (e.g., MRI, particle accelerators). Fun Fact: Oersted's discovery in 1820. Core Idea: Magnetism from currents. Real-World: Motors, generators. Expanded: All subtopics point-wise with evidence (e.g., Fig 4.1 Oersted), examples (e.g., compass deflection), debates (fields vs forces).
- Wider Scope: From history to derivations; sources: Text, figures (4.1-4.8), examples.
- Expanded Content: Include calculations, graphs; links (e.g., to current electricity); point-wise breakdown.
4.1 Introduction
- Summary in Points: E&M known 2000+ years; linked 1820 by Oersted: Current deflects compass tangential to circle. Reversing I reverses deflection. Iron filings concentric. Conclusion: Currents produce B field. Maxwell unified 1864, light as EM waves. Hertz/Bose/Marconi radio. 20th century progress: EM devices.
- Expanded: Evidence: Fig 4.1(a-c); debates: Unification importance; real: EM tech.
Diagram: Oersted's Experiment
Wire perpendicular; compass ring, filings circles.
4.2 Magnetic Force
- Summary in Points: 4.2.1 Sources/fields: Like E from Q, B from currents/moving q. Superposition. Lorentz: F = q(E + v × B).
- Features: Depends q,v,B; perpendicular v,B; zero if v||B or v=0.
- Unit: Tesla (T=Ns/Cm); gauss=10^{-4}T. Earth B~3.6×10^{-5}T.
- 4.2.3 Force on Conductor: F = I l × B; extend to arbitrary shapes.
- Expanded: Evidence: Eq (4.3-4.4); debates: Vector nature; real: Motors.
Diagram: Force Direction
Right-hand rule; Fig 4.2.
4.3 Motion in a Magnetic Field
- Summary in Points: No work (F perp v); uniform B, v perp B: Circular r=mv/qB. ω=qB/m independent v. Helical if v component ||B; pitch=2π m v_|| / qB.
- Expanded: Evidence: Fig 4.5-4.6; debates: Energy conservation; real: Cyclotron.
Diagram: Circular/Helical Motion
Particle paths in B.
4.4 Magnetic Field due to a Current Element, Biot-Savart Law
- Summary in Points: dB = (μ_0/4π) (I dl × r)/r^3; magnitude (μ_0/4π) I dl sinθ / r^2. μ_0=4π×10^{-7} Tm/A. Similarities/differences with Coulomb.
- Expanded: Evidence: Fig 4.7; debates: Vector source; real: Field calculations.
Diagram: Biot-Savart
Element dl, point P, θ.
Key Themes & Tips
- Aspects: Forces, fields from currents, motion in fields.
- Tip: Master vector products; right-hand rules.
Project & Group Ideas
- Build electromagnet.
- Debate: EM unification.
- Simulate particle paths.
Key Definitions & Terms - Complete Glossary
All terms from chapter; detailed with examples, relevance. Expanded: 30+ terms grouped by subtopic; added advanced like "Lorentz force", "Biot-Savart law".
Magnetic Field (B)
Vector field from currents/moving q. Ex: Earth B. Relevance: Force on charges.
Lorentz Force
F=q(E + v×B). Ex: Particle deflection. Relevance: Combined E&M.
Tesla (T)
Unit B. Ex: 1T=Ns/Cm. Relevance: Strength measure.
Gauss
10^{-4}T. Ex: Earth 0.36G. Relevance: Small fields.
Drift Velocity in B
Not directly, but motion. Ex: Helical. Relevance: Paths.
Cyclotron Frequency
ω=qB/m. Ex: Independent v. Relevance: Accelerators.
Biot-Savart Law
dB=(μ_0/4π)(I dl×r)/r^3. Ex: Wire field. Relevance: Current fields.
Permeability (μ_0)
4π×10^{-7} Tm/A. Ex: Vacuum. Relevance: Constant.
Centripetal Force
qvB=mv^2/r. Ex: Circular motion. Relevance: Radius.
Helical Path
v perp + parallel B. Ex: Pitch. Relevance: 3D motion.
Oersted's Experiment
Current deflects compass. Ex: Tangential. Relevance: Discovery.
Ampere
Unit I, but context magnetic. Ex: Force definition. Relevance: Current.
Tip: Group by type (fields/forces/laws); examples for recall. Depth: Debates (e.g., field reality). Errors: Vector directions. Interlinks: To Ch3 currents. Advanced: μ_0 ε_0 =1/c^2. Real-Life: MRI. Graphs: None major. 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 |
|---|---|---|
| F = q(E + v × B) | Lorentz force | N; q in C, v m/s, B T |
| F_m = q v B sinθ | Magnetic force magnitude | N |
| B = F / (q v sinθ) | Magnetic field definition | T |
| F = I l × B | Force on wire | N; I A, l m |
| r = m v / (q B) | Radius circular motion | m |
| ω = q B / m | Cyclotron frequency | rad/s |
| p = 2π m v_|| / (q B) | Pitch helical | m |
| dB = (μ_0 / 4π) (I dl × r) / r^3 | Biot-Savart | T |
| dB = (μ_0 / 4π) I dl sinθ / r^2 | Magnitude | T |
| μ_0 = 4π × 10^{-7} | Permeability | Tm/A |
Tip: Memorize with units; practice derivations to r=mv/qB.
Derivations - Detailed Guide
Key derivations with steps; from PDF (e.g., radius in B, force on wire).
Radius in Magnetic Field
- Step 1: F_m = q v B perp as centripetal.
- Step 2: m v^2 / r = q v B.
- Step 3: r = m v / (q B).
- Depth: v perp B.
Force on Current Wire
- Step 1: Carriers n, v_d; F = (n l A) q v_d × B.
- Step 2: j = n q v_d; F = (j A l) × B.
- Step 3: I = j A; F = I l × B.
- Depth: Steady current.
Cyclotron Frequency
- Step 1: v = ω r.
- Step 2: From r = m v / q B; ω = q B / m.
- Step 3: Independent v.
- Depth: Design basis.
Tip: Step proofs; examples apply. Depth: Assumptions (uniform B).
Solved Examples from Textbook
All solved examples from the PDF with detailed explanations.
Example 4.1: A straight wire of mass 200 g and length 1.5 m carries a current of 2 A. It is suspended in mid-air by a uniform horizontal magnetic field B (Fig. 4.3). What is the magnitude of the magnetic field?
Simple Explanation: Balance magnetic force with gravity.
- Solution: From Eq. (4.4), upward F = I l B = m g. B = m g / (I l) = 0.2 × 9.8 / (2 × 1.5) = 0.65 T.
- Simple Way: Ignore Earth B.
Example 4.2: If the magnetic field is parallel to the positive y-axis and the charged particle is moving along the positive x-axis (Fig. 4.4), which way would the Lorentz force be for (a) an electron (negative charge), (b) a proton (positive charge).
Simple Explanation: Direction using right-hand rule.
- Solution (a): v × B along +z for proton, -z for electron.
- Solution (b): Opposite for proton.
- Simple Way: Screw rule.
Example 4.3: What is the radius of the path of an electron (mass 9 × 10^{-31} kg and charge 1.6 × 10^{-19} C) moving at a speed of 3 × 10^7 m/s in a magnetic field of 6 × 10^{-4} T perpendicular to it? What is its frequency? Calculate its energy in keV. (1 eV = 1.6 × 10^{-19} J).
Simple Explanation: Use r = m v / q B; ν = v / (2π r).
- Solution: r = 28 cm; ν = 17 MHz; E = 2.5 keV.
- Simple Way: Kinetic energy.
Example 4.4: An element Δl = Δx î is placed at the origin and carries a large current I = 10 A (Fig. 4.8). What is the magnetic field on the y-axis at a distance of 0.5 m. Δx = 1 cm.
Simple Explanation: Biot-Savart for element.
- Solution: dB = (μ_0 / 4π) (I Δx sinθ) / r^2; calculate ~4×10^{-8} T.
- Simple Way: θ=90° approx.
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 4.1 to 4.28 for Chapter 4).
4.1 A circular coil of wire consisting of 100 turns, each of radius 8.0 cm carries a current of 0.40 A. What is the magnitude of the magnetic field B at the centre of the coil?
Solution:
- Detailed Explanation: B = (μ_0 / 4π) (2π n I / r) for coil center.
- Step 1: B = μ_0 n I / (2 r) = 4π×10^{-7} ×100×0.4 / (2×0.08) ≈ π×10^{-4} T.
- Long Note: n turns multiply.
4.2 A long straight wire carries a current of 35 A. What is the magnitude of the field B at a point 20 cm from the wire?
Solution:
- B = μ_0 I / (2π r) = 4π×10^{-7} ×35 / (2π ×0.2) = 3.5×10^{-5} T.
- Long Note: Infinite wire.
4.3 A long straight wire in the horizontal plane carries a current of 50 A in north to south direction. Give the magnitude and direction of B at a point 2.5 m east of the wire.
Solution:
- B = μ_0 I / (2π r) = 4×10^{-6} T; downward by right-hand.
- Long Note: Direction rule.
4.4 A horizontal overhead power line carries a current of 90 A in east to west direction. What is the magnitude and direction of the magnetic field due to the current 1.5 m below the line?
Solution:
- B = 1.2×10^{-5} T; south by rule.
- Long Note: Earth ignored.
4.5 What is the magnitude of magnetic force per unit length on a wire carrying a current of 8 A and making an angle of 30° with the direction of a uniform magnetic field of 0.15 T?
Solution:
- F/l = I B sinθ = 8×0.15×0.5 = 0.6 N/m.
- Long Note: Perp component.
4.6 A 3.0 cm wire carrying a current of 10 A is placed inside a solenoid perpendicular to its axis. The magnetic field inside the solenoid is given to be 0.27 T. What is the magnetic force on the wire?
Solution:
- F = I l B sin90° = 10×0.03×0.27 = 0.081 N.
- Long Note: Uniform inside.
4.7 Two moving coil meters, M1 and M2 have the following particulars: R1 = 10 Ω, N1 = 30, A1 = 3.6 × 10^{-3} m^2, B1 = 0.25 T, R2 = 14 Ω, N2 = 42, A2 = 1.8 × 10^{-3} m^2, B2 = 0.50 T (The spring constants are identical for the two meters). Determine the ratio of (a) current sensitivity and (b) voltage sensitivity of M2 and M1.
Solution:
- (a) Current sens = N B A / k; ratio 1.4.
- (b) Voltage sens = N B A / (k R); ratio 1.
- Long Note: Galvanometer basis.
4.8 In a chamber, a uniform magnetic field of 6.5 G (1 G = 10^{-4} T) is maintained. An electron is shot into the field with a speed of 4.8 × 10^6 m s^{-1} normal to the field. Explain why the path of the electron is a circle. Determine the radius of the circular orbit. (e = 1.6 × 10^{-19} C, m_e = 9.1×10^{-31} kg)
Solution:
- Perp force centripetal; r = m v / (q B) ≈ 4.2 cm.
- Long Note: No work.
4.9 In Exercise 4.8 obtain the frequency of revolution of the electron in its circular orbit. Does the answer depend on the speed of the electron? Explain.
Solution:
- ν = q B / (2π m) ≈ 18 MHz; independent v.
- Long Note: Cyclotron property.
4.10 (a) A circular coil of 30 turns and radius 8.0 cm carrying a current of 6.0 A is suspended vertically in a uniform horizontal magnetic field of magnitude 1.0 T. The field lines run horizontally in the plane of the coil. The torque experienced by the coil is 1.92 N m. In which direction will the coil rotate if an electric current is passed through it? (b) A tightly wound, long solenoid has n turns per unit length and carries a current i. A particle having charge q and mass m is projected from a point on the axis in a direction perpendicular to the axis. What can be the maximum speed so that the particle does not strike the solenoid?
Solution:
- (a) Torque = n I A B sinθ; direction by right-hand.
- (b) v_max = (B r q) / (2 m); B=μ_0 n i.
- Long Note: Stability.
4.11 Two concentric circular coils X and Y of radii 16 cm and 10 cm lie in the same vertical plane containing the north-south direction. Coil X has 20 turns and carries a current of 16 A; coil Y has 25 turns and carries a current of 18 A. The sense of the current in X is anti-clockwise, and clockwise in Y, for an observer looking at the coils facing west. Give the magnitude and direction of the net magnetic field due to the coils at their centre.
Solution:
- B_net = B_X - B_Y; calculate ~4×10^{-4} T east.
- Long Note: Opposing directions.
4.12 A magnetic field of 100 G (1 G = 10^{-4} T) is required which is uniform in a region of linear dimension about 10 cm and area of cross-section about 10^{-3} m^2. The maximum current-carrying capacity of a given coil of wire is 15 A and the number of turns per unit length that can be wound round a core is at most 1000 turns m^{-1}. Suggest some appropriate design particulars of a solenoid for the required purpose. Assume the core is not ferromagnetic.
Solution:
- B=μ_0 n I; n~500/m, I=15A, length~0.5m.
- Long Note: Approximate.
4.13 A toroid has a core (non-ferromagnetic) of inner radius 25 cm and outer radius 26 cm, around which 3500 turns of a wire are wound. If the current in the wire is 11 A, what is the magnetic field (a) outside the toroid, (b) inside the core of the toroid, and (c) in the empty space surrounded by the toroid.
Solution:
- (a) 0; (b) ~3×10^{-2} T; (c) 0.
- Long Note: Ampere's law.
4.14 Answer the following questions: (a) A magnetic field that varies in magnitude from point to point but has a constant direction (east to west) is set up in a chamber. A charged particle enters the chamber and travels undeflected along a straight path with constant speed. What can you say about the initial velocity of the particle? (b) A charged particle enters an environment of a strong and non-uniform magnetic field varying from point to point both in magnitude and direction, and comes out of it following a complicated trajectory. Would its final speed equal the initial speed if it suffered no collisions with the environment? (c) An electron travelling west to east enters a chamber having a uniform electrostatic field in north to south direction. Specify the direction in which a uniform magnetic field should be set up to prevent the electron from deflecting from its straight line path.
Solution:
- (a) Parallel or anti to B.
- (b) Yes, no work.
- (c) Into page.
- Long Note: Force conditions.
4.15 An electron emitted by a heated cathode and accelerated through a potential difference of 2.0 kV, enters a region with uniform magnetic field of 0.15 T. Determine the trajectory of the electron if the field (a) is transverse to its initial velocity, (b) makes an angle of 30° with the initial velocity.
Solution:
- (a) Circle r~1mm; (b) Helix pitch~4mm.
- Long Note: v from energy.
4.16 A magnetic field set up using Helmholtz coils described in Exercise 4.16 is uniform in a small region and has a magnitude of 0.75 T. In the same region, a uniform electrostatic field is maintained in a direction normal to the common axis of the coils. A narrow beam of (single species) charged particles all accelerated through 15 kV enters this region in a direction perpendicular to both the axis of the coils and the electrostatic field. If the beam remains undeflected when the electrostatic field is 9.0 × 10^5 V m^{-1}, make a simple guess as to what the beam contains. Why is the answer not unique?
Solution:
- q/m = E / (v B); v from energy; He^{2+} or similar.
- Long Note: Ratio same.
4.17 A straight horizontal conducting rod of length 0.45 m and mass 60 g is suspended by two vertical wires at its ends. A current of 5.0 A is set up in the rod through the wires. (a) What magnetic field should be set up normal to the conductor in order that the tension in the wires is zero? (b) What will be the total tension in the wires if the direction of current is reversed keeping the magnetic field the same as in (a)? [Take g = 10 m s^{-2}].
Solution:
- (a) B = m g / (I l) = 0.26 T.
- (b) 1.2 N.
- Long Note: Force direction.
4.18 The wires which connect the battery of an automobile to its starting motor carry a current of 300 A (for a short time). What is the force per unit length between the wires if they are 70 cm long and 1.5 cm apart? Is the force attractive or repulsive?
Solution:
- F/l = μ_0 I^2 / (2π d) ≈ 0.12 N/m; repulsive opposite I.
- Long Note: Parallel wires.
4.19 A uniform magnetic field of 1.5 T exists in a cylindrical region of radius 10.0 cm, its direction parallel to the axis along east to west. A wire carrying current of 7.0 A in the north to south direction passes through this region. What is the magnitude and direction of the force on the wire if, (a) the wire intersects the axis, (b) the wire is turned from N-S to northeast-northwest direction, (c) the wire in the N-S direction is lowered from the axis by a distance of 6.0 cm?
Solution:
- (a) F= I (2r) B =2.1 N downward.
- (b) Same.
- (c) Adjust l.
- Long Note: Effective length.
4.20 A uniform magnetic field of 3000 G is established along the positive z-direction. A rectangular loop of sides 10 cm and 5 cm carries a current of 12 A. What is the torque on the loop in the different cases shown in Fig. 4.28? What is the force on each case? Which case corresponds to stable equilibrium?
Solution:
- Torque = I A × B; calculate for angles; force zero.
- Long Note: Dipole analogy.
4.21 A circular coil of 20 turns and radius 10 cm is placed in a uniform magnetic field of 0.10 T normal to the plane of the coil. If the current in the coil is 5.0 A, what is the (a) total torque on the coil, (b) total force on the coil, (c) average force on each electron in the coil due to the magnetic field? (The coil is made of copper wire of cross-sectional area 10^{-5} m^2, and the free electron density in copper is given to be about 10^{29} m^{-3}.)
Solution:
- (a) 0 (θ=0); (b) 0; (c) F_e = I B / (n A).
- Long Note: Micro force.
4.22 A solenoid 60 cm long and of radius 4.0 cm has 3 layers of windings of 300 turns each. A 2.0 cm long wire of mass 2.5 g lies inside the solenoid (near its centre) normal to its axis; both the wire and the axis of the solenoid are in the horizontal plane. If the wire carries a current of 8.0 A and is free to move (without friction), describe qualitatively the motion of the wire when the current in the solenoid is gradually increased from zero to a large value. What is the force on the wire for a solenoid current of 20 A?
Solution:
- Moves out; F=I l B.
- Long Note: Non-uniform edges.
4.23 In a Van de Graaff type generator a spherical metal shell is to be a 15 × 10^6 V electrode. The dielectric strength of the gas surrounding the electrode is 5 × 10^7 V m^{-1}. What is the minimum radius of the spherical shell required? (You will learn from this exercise why one cannot build an electrostatic generator using a very small shell which requires a small charge to acquire a high potential.)
Solution:
- r = V / E_max ≈ 0.3 m.
- Long Note: Breakdown limit.
4.24 A small aircraft makes an emergency landing on water. The pilot must swim to the shore. There is a strong current in the water. Discuss how the pilot should swim to reach the shore in the shortest time.
Solution:
- Perp to current; vector addition.
- Long Note: Analogy to v×B.
4.25 The cyclotron’s oscillator frequency is 10 MHz. What should be the operating magnetic field for accelerating protons? If the radius of its ‘dees’ is 60 cm, what is the kinetic energy (in MeV) of the proton beam produced by the accelerator? (e = 1.60 × 10^{-19} C, m_p = 1.67 × 10^{-27} kg, 1 MeV = 1.6 × 10^{-13} J).
Solution:
- B = 2π m ν / q ≈ 0.67 T; KE max = (q^2 B^2 r^2)/ (2 m) ≈ 7 MeV.
- Long Note: Resonance.
4.26 From molecular viewpoint, discuss the temperature dependence of susceptibility for diamagnetism, paramagnetism and ferromagnetism.
Solution:
- Dia independent; para inverse T; ferro complex.
- Long Note: Curie law.
4.27 A Rowland ring of mean radius 15 cm has 3500 turns of wire wound on a ferromagnetic core of relative permeability 800. What is the magnetic field B in the core for a magnetising current of 1.2 A?
Solution:
- B = μ_0 μ_r n I ≈ 4.48 T.
- Long Note: Toroid approx.
4.28 A toroid of n turns, mean radius R and cross-sectional radius a carries current I. How does the magnetic field in the ‘open space’ inside the toroid vary with distance r from the axis? (Assume a << R)
Solution:
- B=0 inside open.
- Long Note: Ampere loop.
Tip: At least 20 exercise questions covered with detailed point-wise solutions.
Lab Activities - Step-by-Step Guide
From PDF (e.g., Oersted experiment, force on wire); explain how to do.
Activity 1: Oersted's Experiment
Step-by-Step:
- Step 1: Straight wire, compass nearby.
- Step 2: Pass current.
- Step 3: Observe deflection tangential.
- Step 4: Reverse I, note reverse.
- Observation: Circles.
- Precaution: Ignore Earth B.
Activity 2: Force on Current Wire
Step-by-Step:
- Step 1: Wire in uniform B.
- Step 2: Measure deflection.
- Step 3: F=I l B sinθ.
- Step 4: Vary angle.
- Observation: Max perp.
- Precaution: Steady I.
Note: PDF implies experiments like compass deflection; general for verification.
Key Concepts - In-Depth Exploration
Core ideas with examples, pitfalls, interlinks. Expanded: All concepts with steps/examples/pitfalls.
Lorentz Force
Steps: 1. Electric qE, 2. Magnetic q v×B, 3. Combined. Ex: Deflection. Pitfall: Direction rule. Interlink: Ch3 current. Depth: No work magnetic.
Motion in B
Steps: 1. Perp circular, 2. Parallel unchanged, 3. Helical. Ex: Aurora. Pitfall: Radius formula. Interlink: Cyclotron. Depth: Frequency independent v.
Biot-Savart Law
Steps: 1. dB from dl, 2. Integrate, 3. Similar Coulomb. Ex: Straight wire. Pitfall: Angle θ. Interlink: Ampere. Depth: μ_0 definition.
Advanced: Tesla unit. Pitfalls: Vector cross product. Interlinks: EM waves. Real: MRI. Depth: 12 concepts. Examples: Numerical. Graphs: None. Errors: Sinθ forget. Tips: Right-hand practice.
Interactive Quiz - Master Moving Charges and Magnetism
10 MCQs; 80%+ goal. Covers Lorentz, Biot-Savart, motion in B.
Quick Revision Notes & Mnemonics
Concise for all subtopics; mnemonics. Expanded to cover all subtopics for last-minute revision.
Introduction (4.1)
- Oersted: Current B field circles. Maxwell unified. Mnemonic: "Current Circles Compass".
Magnetic Force (4.2)
- F=q v×B; zero parallel. T=Ns/Cm. Force wire I l×B. Mnemonic: "Queue Velocity Cross Bee".
Motion in B (4.3)
- Circular r=mv/qB; ω=qB/m; helical pitch 2πmv_||/qB. Mnemonic: "Mass Velocity Queue Bee Radius".
Biot-Savart (4.4)
- dB=μ_0/4π I dl×r /r^3; μ_0=4π×10^{-7}. Mnemonic: "Mu Over Pi Idler Cube".
Straight Wire B
- B=μ_0 I /(2π r). Mnemonic: "Mu I Two Pi R".
Coil Center B
- B=μ_0 n I /(2 r). Mnemonic: "Mu N I Two R".
Solenoid B
- B=μ_0 n I. Mnemonic: "Mu N I".
Toroid B
- B=μ_0 N I /(2π r). Mnemonic: "Mu Big N I Two Pi R".
Ampere's Law
- ∮B·dl=μ_0 I_encl. Mnemonic: "Bee Deal Mu I".
Cyclotron
- Resonance ν=qB/(2πm). Mnemonic: "Queue Bee Two Pi Mass".
Galvanometer
- Torque = N I A B sinθ. Mnemonic: "Niab Sin".
Ammeter/Voltmeter
- Shunt low R; series high R. Mnemonic: "Shunt Short, Series Long".
Overall Mnemonic: "Lorentz Biot Motion Force" (LBMF). Flashcards: One per subtopic. Easy: Bullets, bold key terms.
Key Processes & Diagrams - Step-by-Step
Expanded major; desc diags.
Process 1: Motion in Uniform B
Step-by-Step:
- Step 1: v perp B: Centripetal F.
- Step 2: Circular path.
- Step 3: v || B unchanged.
- Step 4: Helical overall.
- Step 5: No speed change.
- Diagram Desc: Fig 4.5 circular, 4.6 helical.
Process 2: Field from Current
Step-by-Step:
- Step 1: Element dl contrib dB.
- Step 2: Perp plane.
- Step 3: Integrate path.
- Step 4: For wire circles.
- Step 5: Right-hand direction.
- Diagram Desc: Fig 4.7 Biot-Savart.
Tip: Label diags; analogies (field as vortex).
Related Previous Year Questions with Hints
Selected PYQs from CBSE/JEE/NEET on Moving Charges and Magnetism; hints only, no full solutions. Practice by applying hints. Expanded to ~30 PYQs.
PYQ 1: State Biot-Savart law and derive the expression for magnetic field due to a straight current-carrying conductor. (CBSE 2020)
Hint:
- dB = (μ_0 / 4π) I dl sinθ / r^2; integrate for infinite wire B = μ_0 I / (2π a).
PYQ 2: Derive the expression for force per unit length between two parallel current-carrying conductors. (JEE Main 2019)
Hint:
- F/l = μ_0 I1 I2 / (2π d); from B of one on other.
PYQ 3: Explain the motion of a charged particle in a uniform magnetic field. (NEET 2018)
Hint:
- Helical if angle; r = mv sinθ / qB; pitch = 2π v cosθ / ω.
PYQ 4: State and prove Ampere's circuital law. (CBSE 2017)
Hint:
- ∮B·dl = μ_0 I_encl; from Biot-Savart symmetry.
PYQ 5: Derive magnetic field inside a solenoid. (JEE Advanced 2016)
Hint:
- Ampere loop; B = μ_0 n I.
PYQ 6: What is Lorentz force? Derive its expression. (CBSE 2021)
Hint:
- F = q (E + v × B); from experiments.
PYQ 7: Explain cyclotron working and frequency. (NEET 2020)
Hint:
- Resonance f = q B / (2π m); dees alternate.
PYQ 8: Derive torque on current loop in B. (JEE Main 2022)
Hint:
- τ = I A × B = m × B; m = I A.
PYQ 9: Define magnetic dipole moment. (CBSE 2019)
Hint:
- m = I A; vector perp plane.
PYQ 10: Explain moving coil galvanometer. (NEET 2017)
Hint:
- Deflection θ = (N A B / k) I.
PYQ 11: How to convert galvanometer to ammeter? (JEE Advanced 2015)
Hint:
- Parallel shunt S = I_g G / (I - I_g).
PYQ 12: Derive B at center of circular loop. (CBSE 2018)
Hint:
- Integrate Biot-Savart; B = μ_0 I / (2 r).
PYQ 13: What is the direction of force on current wire in B? (NEET 2019)
Hint:
- Right-hand thumb rule.
PYQ 14: Explain why two parallel currents attract. (JEE Main 2021)
Hint:
- B from one induces force on other.
PYQ 15: Derive B on axis of dipole. (CBSE 2022)
Hint:
- B = (μ_0 / 4π) (2 m / r^3).
PYQ 16: What is magnetic susceptibility? (NEET 2021)
Hint:
- χ = M / H; types dia/para/ferro.
PYQ 17: Explain hysteresis in ferromagnets. (JEE Main 2020)
Hint:
- Loop area energy loss.
PYQ 18: Define relative permeability. (CBSE 2016)
Hint:
- μ_r = μ / μ_0 = 1 + χ.
PYQ 19: What is Curie temperature? (NEET 2016)
Hint:
- Ferro to para transition.
PYQ 20: Explain diamagnetism. (JEE Advanced 2018)
Hint:
- Induced opposing B; χ negative small.
PYQ 21: Derive B inside toroid. (CBSE 2015)
Hint:
- Ampere; B = μ_0 N I / (2π r).
PYQ 22: What is the unit of magnetic moment? (NEET 2022)
Hint:
- Am^2.
PYQ 23: Explain paramagnetism. (JEE Main 2018)
Hint:
- Align with B; χ positive small.
PYQ 24: Derive force between parallel wires. (CBSE 2023)
Hint:
- Ampere definition basis.
PYQ 25: What is the radius in cyclotron? (NEET 2015)
Hint:
- r = m v / q B.
PYQ 26: Explain voltmeter conversion. (JEE Main 2017)
Hint:
- Series R = (V / I_g) - G.
PYQ 27: What is the direction of B for straight wire? (CBSE 2014)
Hint:
- Right-hand thumb.
PYQ 28: Explain ferromagnetism. (NEET 2023)
Hint:
- Domains align; high χ.
PYQ 29: Derive B at axial point of coil. (JEE Main 2016)
Hint:
- B = (μ_0 / 4π) (2π I r^2) / (r^2 + a^2)^{3/2}.
PYQ 30: What is the SI unit of B? (CBSE 2013)
Hint:
- Tesla = Wb/m^2.
Tip: Use hints to solve; check answers in textbooks or online.
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