Your learning path
Follow the steps in order. Each link opens a page on eduPhysics.
- Notes: Moving Charges and MagnetismChapter-wise notes to build the concepts first.
- Moving Charges & Magnetism: The Ultimate Learning EcosystemLorentz force, Biot–Savart, Ampere’s law, cyclotron, solved numericals and MCQs.
- NCERT Book Back Exercise SolutionsEvery NCERT exercise solved step by step for boards, NEET and JEE Main.
- PYQs: Moving Charges and MagnetismExam practice with previous-year questions.
- Notes: Magnetism and MatterBar magnets, earth’s magnetism and magnetic materials.
- PYQs: Magnetism and MatterTest yourself on the second chapter.
Moving charges and magnetism
Force on a moving charge
A charge q moving with velocity v in a magnetic field B feels a force that is perpendicular to both. The magnetic force does no work, so it changes the direction of the velocity but not the speed.
Motion in a uniform field
Perpendicular to B
The charge moves in a circle.
The time period does not depend on speed, which is the idea behind the cyclotron.
At an angle θ to B
The charge follows a helix.
The component along B is unaffected and sets the pitch.
Fields produced by currents
- Biot–Savart law: dB = (μ₀/4π) I dl sinθ / r². It gives the field of any current element.
- Long straight wire: B = μ₀I / 2πr, with direction given by the right-hand grip rule.
- Circular loop: B = μ₀I / 2R at the centre.
- Ampere’s circuital law: ∮B·dl = μ₀Ienclosed, used for symmetrical cases.
- Solenoid: B = μ₀nI inside. Toroid: B = μ₀NI / 2πr.
Forces and torque on currents
- Wire in a field: F = BIl sinθ.
- Two parallel wires: F/l = μ₀I₁I₂ / 2πd. Currents in the same direction attract; opposite directions repel. This defines the ampere.
- Current loop: magnetic moment m = NIA and torque τ = NIAB sinθ.
- Moving coil galvanometer: current sensitivity θ/I = NAB/k. Convert it to an ammeter with a shunt and to a voltmeter with a series resistance.
Magnetism and matter
- Bar magnet: it behaves like a current loop with magnetic moment m. On its axis B = μ₀·2m / 4πr³, and on its equatorial line B = μ₀·m / 4πr³.
- Dipole in a field: τ = mB sinθ and potential energy U = −mB cosθ.
- Gauss’s law for magnetism: ∮B·dA = 0, since there are no isolated magnetic poles.
- Earth’s magnetism: the horizontal component BH = BE cosδ, and tanδ = BV/BH, where δ is the angle of dip.
- Magnetic materials: B = μ₀(H + M), χ = M/H and μr = 1 + χ.
| Material | Susceptibility χ | Behaviour |
|---|---|---|
| Diamagnetic | small and negative | Weakly repelled by a magnet; Curie’s law does not apply |
| Paramagnetic | small and positive | Weakly attracted; χ = C/T (Curie’s law) |
| Ferromagnetic | large and positive | Strongly attracted; shows hysteresis; loses magnetism above the Curie temperature |
The hysteresis loop gives retentivity and coercivity. Soft iron has low coercivity, so it suits electromagnets and transformer cores. Steel has high coercivity, so it suits permanent magnets.
Quick formula sheet
| Quantity | Formula |
|---|---|
| Lorentz force | F = q(E + v × B) |
| Radius of circular path | r = mv / qB |
| Cyclotron frequency | f = qB / 2πm |
| Field of long wire | B = μ₀I / 2πr |
| Field of solenoid | B = μ₀nI |
| Force between parallel wires | F/l = μ₀I₁I₂ / 2πd |
| Torque on a loop | τ = NIAB sinθ |
| Ammeter shunt | S = IgG / (I − Ig) |
| Voltmeter series resistance | R = V/Ig − G |
| Dipole torque | τ = mB sinθ |
| Dip angle | tanδ = BV / BH |
| Curie’s law | χ = C / T |
For every chapter on one page, use the Physics Formula Sheet Master Hub.
Worked numericals
1. A proton moves at 2 × 10⁶ m/s perpendicular to a field of 0.1 T. Find the force, the radius and the time period.
F = qvB = (1.6×10⁻¹⁹)(2×10⁶)(0.1) = 3.2 × 10⁻¹⁴ N.
r = mv/qB = (1.67×10⁻²⁷)(2×10⁶) / (1.6×10⁻¹⁹ × 0.1) ≈ 0.21 m.
T = 2πm/qB ≈ 6.6 × 10⁻⁷ s.
2. A solenoid has 500 turns per metre and carries 2 A. Find the field inside it.
B = μ₀nI = (4π×10⁻⁷)(500)(2) ≈ 1.26 × 10⁻³ T.
3. Two long parallel wires 10 cm apart carry 5 A and 10 A in the same direction. Find the force per metre.
F/l = μ₀I₁I₂/2πd = (2×10⁻⁷)(5)(10) / 0.1 = 1 × 10⁻⁴ N/m, and the wires attract.
4. A coil of 100 turns and area 0.01 m² carries 0.5 A in a field of 0.2 T, with its plane parallel to the field. Find the torque.
The plane is parallel to B, so θ = 90° between the moment and the field. τ = NIAB = 100 × 0.5 × 0.01 × 0.2 = 0.1 N m.
Quick questions
Why does a magnetic force do no work on a moving charge?
The force is always perpendicular to the velocity, so the displacement along the force is zero. The speed and kinetic energy stay the same, and only the direction changes.
Why is the time period of a charge in a magnetic field independent of its speed?
A faster charge moves on a larger circle, in exact proportion to its speed, so the time for one revolution, T = 2πm/qB, stays the same. This is why a cyclotron can use a fixed-frequency electric field.
Do two parallel wires with currents in the same direction attract or repel?
They attract. The field of one wire exerts a force on the other that points towards it. Opposite currents repel.
Why is there no magnetic monopole in Gauss’s law for magnetism?
Magnetic field lines form closed loops, so the net flux through any closed surface is zero. Cutting a magnet only produces two smaller magnets, each with a north and a south pole.
Why is soft iron used for electromagnets and steel for permanent magnets?
Soft iron has low retentivity and coercivity, so it magnetises and demagnetises easily. Steel has high coercivity, so it keeps its magnetism.
Go deeper: the Ultimate Success Pack
Moving Charges and Magnetism: Ultimate Success Pack
A 504-page, exam-focused resource for CBSE Class 12, NEET and JEE Main. It brings the chapter together in one workflow, from concepts to practice and revision.
- Clear chapter notes and formula revision
- Visual mind maps and essential diagrams
- Solved numericals and MCQs
- PYQs and assertion-and-reason questions