Menu

Moving Charges and Magnetism

NCERT Class 12 Physics Chapter 4

Moving Charges and Magnetism for Class 12 Physics, JEE and NEET: Lorentz force, Biot–Savart and Ampere’s laws, solenoids and the moving coil galvanometer.

10 topics Updated 8 Nov 2026

For: Class 12, JEE and NEET, unless a topic says otherwise

In the syllabus: JEE Class 12 syllabus, NEET Class 12 syllabus

With your textbook

NCERT Physics Part I (Class 12), Chapter 4 “Moving Charges and Magnetism”, reprint 2026-27.

Open the official NCERT chapter (PDF, 3.7 MB, ncert.nic.in)

Checked on 19 Oct 2026.

Learn in this order

  1. Magnetic force and the Lorentz force

    F = q(E + v × B), magnetic force |q|vB sin θ, directions, the tesla and force on a wire, with examples.

    NCERT Sections 4.1–4.2 14 min read 4 solved examples 8 practice questions

  2. Motion of a charge in a magnetic field

    Why a charge circles, r = mv/(qB), frequency qB/(2πm), helical paths and the pitch, with examples.

    NCERT Section 4.3 12 min read 4 solved examples 8 practice questions

  3. Biot–Savart law: the field of a current element

    The statement and vector form, dB = μI dl sin θ/(4πr), direction of dB, μ and Coulomb’s law, with examples.

    NCERT Section 4.4 11 min read 4 solved examples 7 practice questions

  4. Magnetic field on the axis of a circular current loop

    Formula and derivation, μI/(2R) at the centre, arcs, N turns and direction.

    NCERT Section 4.5 12 min read 4 solved examples 8 practice questions

  5. Ampere’s circuital law

    Statement and sign rule, amperian loops, B = μI/(2πr) for a long wire, B inside a thick wire, examples.

    NCERT Section 4.6 13 min read 4 solved examples 8 practice questions

  6. The solenoid

    B = μnI from Ampere’s law, uniform inside and nearly zero outside, direction, ends, examples.

    NCERT Section 4.7 10 min read 4 solved examples 7 practice questions

  7. Force between two parallel currents and the ampere

    Derivation of the force per metre, why like currents attract, and the ampere’s definition.

    NCERT Section 4.8 11 min read 4 solved examples 7 practice questions

  8. Torque on a current loop and the magnetic dipole

    Derivation of τ = IAB sin θ, magnetic moment m = NIA, τ = m × B, and the loop as a magnetic dipole.

    NCERT Section 4.9 15 min read 4 solved examples 8 practice questions

  9. The moving coil galvanometer

    The radial field, φ = (NAB/k)I, conversion to an ammeter and a voltmeter, and its sensitivity.

    NCERT Section 4.10 13 min read 4 solved examples 7 practice questions

  10. Experiment: resistance and figure of merit of a galvanometer

    The half-deflection method, G = RS/(R − S), k = ε/[(R + G)θ], precautions, examples.

    JEE and NEET only 10 min read 4 solved examples 7 practice questions

Key formulas in this chapter

Magnetic force

  • F = q(E + v × B)
  • F = |q|vB sin θ
  • F = I l × B
  • F = IlB sin θ
  • 1 T = 1 N s C m = 10 G

Motion in a magnetic field

  • r = mv/(qB)
  • ω = 2πν = qB/m
  • T = 2πm/(qB)
  • pitch: p = 2πm v cos θ/(qB)
  • r = √(2mK)/(qB)

Biot–Savart law

  • vector form: dB = (μ/4π) I dl × r/r
  • dB = μ I dl sin θ/(4πr)
  • μ/4π ≈ 10 T m/A
  • εμ = 1/c
  • dB = 0 along the line of the element

Field on the axis of a loop

  • B = μ0 I R2/[2(x2 + R2)3/2]
  • B0 = μ0 I/(2R)
  • N turns: B = μNI/(2R)
  • arc of angle φ: B = μIφ/(4πR)
  • far on the axis: B ≈ μIR/(2x)

Ampere’s circuital law

  • ∮ B · dl = μI
  • BL = μ0 Ie
  • B = μI/(2πr)
  • inside a uniform wire: B = μIr/(2πa)
  • B ∝ r inside, ∝ 1/r outside

The solenoid

  • B = μnI
  • n = N/l
  • Bh = μI(nh)
  • at an end: B ≈ μnI/2
  • outside a long solenoid: B ≈ 0

Force between parallel currents

  • F = μ0 Ia Ib L/(2πd)
  • f = μ0 Ia Ib/(2πd)
  • Fba = −Fab
  • 1 A, 1 m apart: f = 2 × 10 N/m
  • same direction attract, opposite repel

Torque on a current loop

  • τ = IAB sin θ
  • m = NIA
  • τ = m × B
  • U = −m · B
  • far on the axis: B = (μ/4π)(2m/x)

Moving coil galvanometer

  • kφ = NIAB
  • φ/I = NAB/k
  • φ/V = NAB/(kRG)
  • shunt: rs = Ig RG/(I − Ig)
  • voltmeter: R = V/Ig − RG

Experiment: galvanometer resistance

  • G = RS/(R − S) ≈ S (R ≫ S)
  • k = ε/[(R + G)θ]
  • current sensitivity = 1/k
  • I1 = ε/(R + G)
  • full scale: Ig = k × divisions

More in Physics