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Moving Charges and Magnetism – Class 12 Physics Chapter 4 Notes & NCERT PDF

Class 12PhysicsChapter 4NCERT book: Physics Part I - Class 12

Notes and a simple summary of Chapter 4 of the NCERT Class 12 Physics book, with the official chapter PDF, flashcards, an MCQ quiz and an AI tutor for your doubts.

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Chapter 4: Moving Charges and Magnetism

Introduction

Chapter 4 starts from Oersted's 1820 discovery that a current-carrying wire deflects a compass needle — moving charges produce magnetic fields. The chapter covers the force on moving charges and currents (Lorentz force), circular motion of charges in a field, the fields produced by currents (Biot–Savart law and Ampere's circuital law), forces between parallel currents, torque on a current loop, and the moving coil galvanometer.

Key Concepts

4.2 Magnetic force — the Lorentz force

A charge q moving with velocity v in fields E and B experiences F = q[E + v × B].

  • The magnetic part F = q(v × B) has magnitude qvB sin θ, is perpendicular to both v and B, is zero for a charge at rest or moving parallel to B, and does no work (it changes only the direction of motion).
  • SI unit of B: tesla (T); 1 gauss = 10⁻⁴ T. Earth's field is about 3.6 × 10⁻⁵ T.
  • Force on a current-carrying conductor: F = Il × B, magnitude BIl sin θ.

    • 4.3 Motion in a magnetic field

    If v ⟂ B, the charge moves in a circle: qvB = mv²/r → r = mv/(qB). The angular frequency ω = qB/m and frequency ν = qB/(2πm) do not depend on speed — the principle behind the cyclotron. If v has a component along B, the path is a helix with pitch p = 2πmv_∥/(qB).

    4.4 Biot–Savart law

    The field of a current element: dB = (μ₀/4π) I dl × r/r³, with μ₀ = 4π × 10⁻⁷ T m A⁻¹. Magnitude dB = (μ₀/4π) I dl sin θ/r².

    4.5 Field on the axis of a circular loop

    B = μ₀IR²/[2(x² + R²)^(3/2)], directed along the axis. At the centre (x = 0), B = μ₀I/(2R); for N turns, B = μ₀NI/(2R). The direction is given by the right-hand thumb rule (curl fingers along the current; thumb points along B).

    4.6 Ampere's circuital law

    ∮B·dl = μ₀I_enclosed. It plays the role Gauss's law played in electrostatics — useful when there is symmetry.

  • Long straight wire: B = μ₀I/(2πr), field lines are concentric circles.

    • 4.7 The solenoid

    A long, tightly wound solenoid with n turns per unit length has a uniform field inside, B = μ₀nI, along its axis, and a negligible field outside.

    4.8 Force between two parallel currents

    Force per unit length f = μ₀I_aI_b/(2πd). Like (parallel) currents attract; antiparallel currents repel. This defines the ampere: the current which, in two infinitely long parallel wires 1 m apart in vacuum, produces a force of 2 × 10⁻⁷ N per metre.

    4.9 Torque on a current loop — magnetic dipole

    A rectangular loop of area A with N turns in a uniform field experiences no net force but a torque τ = m × B, magnitude NIAB sin θ, where m = NIA is the magnetic moment (unit A m²). A circular current loop therefore behaves like a magnetic dipole.

    4.10 The moving coil galvanometer

    A coil in a radial field (concave pole pieces and a soft-iron core) keeps the torque NIAB independent of orientation. At equilibrium NIAB = kφ, so φ = (NAB/k) I — the deflection is proportional to current.

  • Current sensitivity: φ/I = NAB/k.
  • Converting to an ammeter: connect a small shunt resistance r_s in parallel: r_s = I_gG/(I − I_g).
  • Converting to a voltmeter: connect a large resistance R in series: R = V/I_g − G.

    • Worked Examples

  • Example 4.1 (suspended wire): a 200 g wire, 1.5 m long, carrying 2 A floats in a horizontal field when BIl = mg → B = (0.2 × 9.8)/(2 × 1.5) ≈ 0.65 T.
  • Example 4.3 (circular motion): an electron (m = 9 × 10⁻³¹ kg) at 3 × 10⁷ m s⁻¹ in B = 6 × 10⁻⁴ T ⟂ v: r = mv/(eB) ≈ 0.28 m, ν = v/(2πr) ≈ 1.7 × 10⁷ Hz, kinetic energy ½mv² ≈ 2.5 keV.
  • Example 4.6 (coil): 100 turns, radius 10 cm, 1 A: B = μ₀NI/(2R) = 4π × 10⁻⁷ × 100 × 1/(0.2) ≈ 6.28 × 10⁻⁴ T at the centre.
  • Example 4.8 (solenoid): 500 turns over 0.5 m (n = 1000 m⁻¹), I = 5 A: B = μ₀nI ≈ 6.28 × 10⁻³ T inside.
  • Galvanometer conversion: G = 100 Ω, full-scale I_g = 1 mA. To read 1 A, shunt r_s = I_gG/(I − I_g) ≈ 0.1 Ω; to read 10 V, series R = V/I_g − G = 9900 Ω.

    • Formula / Key-Facts Sheet

  • F = q(v × B); on a wire F = Il × B
  • r = mv/(qB); ω = qB/m (independent of v)
  • Biot–Savart: dB = (μ₀/4π) I dl sin θ/r²; μ₀ = 4π × 10⁻⁷ T m A⁻¹
  • Loop centre B = μ₀NI/2R; axis B = μ₀IR²/2(x² + R²)^(3/2)
  • Straight wire B = μ₀I/2πr; solenoid B = μ₀nI
  • Parallel wires f = μ₀I₁I₂/2πd
  • τ = NIAB sin θ; m = NIA
  • Shunt r_s = I_gG/(I − I_g); series R = V/I_g − G

    • Board Exam Focus

  • Numericals: radius and frequency of a charged particle, field at the centre of a coil or inside a solenoid, force between parallel wires, galvanometer conversion.
  • Derivations: field on the axis of a circular loop (Biot–Savart); field of a long wire and a solenoid (Ampere's law); force between parallel conductors and the definition of the ampere; torque on a rectangular loop.
  • Answer outline — force between parallel wires: wire a produces B_a = μ₀I_a/2πd at wire b → force on length L of b is I_bLB_a → per unit length f = μ₀I_aI_b/2πd, attractive for parallel currents.
  • Answer outline — why a radial field: it keeps the plane of the coil parallel to B, so torque = NIAB for all deflections and the scale is linear.
  • Conceptual: why the magnetic force does no work; why the ammeter has low and the voltmeter high resistance.

    • Key Terms

    Magnetic field (चुंबकीय क्षेत्र), Lorentz force (लॉरेंज बल), Tesla (टेस्ला), Permeability of free space (निर्वात की चुंबकशीलता), Biot–Savart law (बायो-सावर्ट नियम), Ampere's circuital law (ऐम्पियर का परिपथीय नियम), Solenoid (परिनालिका), Magnetic moment (चुंबकीय आघूर्ण), Magnetic dipole (चुंबकीय द्विध्रुव), Torque (बल आघूर्ण), Galvanometer (गैल्वेनोमीटर), Shunt (शंट), Ammeter (ऐमीटर), Voltmeter (वोल्टमीटर), Radial field (त्रिज्य क्षेत्र)

    Common Mistakes

  • Forgetting that the magnetic force on an electron is opposite to that on a proton for the same v and B.
  • Assuming the magnetic force changes a particle's speed (it changes only direction).
  • Using μ₀I/2πr (wire) for the centre of a loop (correct is μ₀I/2R).
  • Connecting the shunt in series or the ammeter-conversion resistance in parallel.
  • Mixing up attraction and repulsion for parallel and antiparallel currents.

    • 💡 Key Learning Points

    • ✓Lorentz force on moving charges and force on current-carrying conductors
    • ✓Circular and helical motion of charged particles in a magnetic field
    • ✓Biot–Savart law and field on the axis of a circular loop
    • ✓Ampere's circuital law applied to a straight wire and a solenoid; force between parallel currents
    • ✓Torque on current loops, magnetic moment and the moving coil galvanometer as ammeter/voltmeter

    👨‍🏫 Teaching Tips

    • →Recreate Oersted's experiment with a compass under a current-carrying wire
    • →Use the right-hand rule and Fleming's left-hand rule with physical hand gestures
    • →Show the circular path idea with a charged-particle simulation, then derive r = mv/qB
    • →Derive the loop's axial field carefully, then special-case the centre
    • →Draw the Ampere loop for a wire and a solenoid and compare with Gauss's law
    • →Open a real galvanometer to show the radial field and spring
    • →Practise shunt and series-resistance conversions with numbers

    📋 Assessment Questions

    1. Can students find the direction of magnetic force on positive and negative charges?
    2. Can they derive r = mv/qB and show the frequency is speed-independent?
    3. Can they derive fields of a loop, straight wire and solenoid?
    4. Can they derive the force between parallel wires and define the ampere?
    5. Can they design an ammeter and a voltmeter from a galvanometer?

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    Keep learning

    All chapters in Physics Part I - Class 12

    1. 1. Electric Charges and Fields
    2. 2. Electrostatic Potential and Capacitance
    3. 3. Current Electricity
    4. 4. Moving Charges and Magnetism
    5. 5. Magnetism and Matter
    6. 6. Electromagnetic Induction
    7. 7. Alternating Current
    8. 8. Electromagnetic Waves