Schooling · Class 12 · Physics · Moving Charges and Magnetism · Chapter on a page
CBSE Class 12 · Physics · NCERT Physics Part-I
Moving Charges and Magnetism: chapter on a page
A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).
About the notes: Written by Shishya's AI on 27 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.
This note's current text has no applied fact-check on record.
Mind map
Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.
The mind map as a list
- Key ideas
- A moving charge creates a magnetic…
- The Biot-Savart law gives the…
- Ampere's circuital law states that…
- A straight long wire carrying…
- A circular loop of radius R carrying…
- A solenoid of n turns per unit…
- The Lorentz force on a charge q…
- Formulas and facts
- dB = (μ₀/4π) (I dl sin θ)/r²
- B = μ₀I/(2πr)
- B = μ₀I/(2R)
- B = μ₀nI
- ∮B · dl = μ₀ I_enc
- F = qvB sin θ
- F = BIL sin θ
- Worked examples
- Magnetic field due to a long…
- Motion of a proton in a magnetic field
- Torque on a rectangular coil
- Watch out for
- Confusing the angle in torque formula
- Forgetting that magnetic force on a…
- Using Ampere's law without checking…
- Mixing up the direction rules
- Treating solenoid formula B = μ₀nI…
What this chapter is about
This chapter explores the deep connection between electricity and magnetism. You already know that stationary charges produce electric fields. Here you learn that charges in motion—electric currents—produce magnetic fields and also experience forces when placed in external magnetic fields. This unification of electricity and magnetism was one of the great achievements of nineteenth-century physics.
Key ideas
- A moving charge creates a magnetic field around it; an electric current (many moving charges) produces a magnetic field whose pattern depends on the shape of the conductor.
- The Biot-Savart law gives the magnetic field dB at a point due to a small current element I dl: dB = (μ₀/4π) × (I dl sin θ)/r², directed perpendicular to the plane containing dl and the position vector r, following the right-hand rule.
- Ampere's circuital law states that the line integral of the magnetic field B around any closed loop equals μ₀ times the net current enclosed: ∮B · dl = μ₀ I_enclosed. It is most useful when symmetry simplifies the integral.
- A straight long wire carrying current I produces circular magnetic field lines; at perpendicular distance r, the magnitude is B = μ₀I/(2πr).
- A circular loop of radius R carrying current I produces, at its centre, a field B = μ₀I/(2R), directed along the axis of the loop (use right-hand curl rule).
- A solenoid of n turns per unit length carrying current I produces a nearly uniform field inside: B = μ₀nI, directed along its axis.
- The Lorentz force on a charge q moving with velocity v in a magnetic field B is F = q(v × B). This force is always perpendicular to v, so it changes direction but not speed.
- A current-carrying conductor of length L in a uniform field B experiences force F = I L B sin θ, where θ is the angle between the wire and the field.
- A current loop (magnetic dipole) in a uniform field experiences a torque τ = M × B, where M = NIA is the magnetic moment (N turns, area A).
Formulas and facts to remember
- Formula: dB = (μ₀/4π) (I dl sin θ)/r² · Meaning: Biot-Savart law: field due to a small current element
- Formula: B = μ₀I/(2πr) · Meaning: Field at distance r from a long straight wire
- Formula: B = μ₀I/(2R) · Meaning: Field at the centre of a circular loop of radius R
- Formula: B = μ₀nI · Meaning: Field inside a long solenoid (n = turns per metre)
- Formula: ∮B · dl = μ₀ I_enc · Meaning: Ampere's circuital law
- Formula: F = qvB sin θ · Meaning: Magnitude of Lorentz force on a moving charge
- Formula: F = BIL sin θ · Meaning: Force on a straight current-carrying wire in a field
- Formula: τ = NIAB sin φ · Meaning: Torque on a coil; φ is angle between M and B
- Formula: r = mv/(qB) · Meaning: Radius of circular path of a charge in a uniform field
- Formula: T = 2πm/(qB) · Meaning: Time period of circular motion; independent of speed
- μ₀ = 4π × 10⁻⁷ T m A⁻¹ is the permeability of free space.
Common mistakes
- Confusing the angle in torque formula: the angle φ is between the area vector (normal) and B, not between the plane and B → always draw the normal first.
- Forgetting that magnetic force on a moving charge is perpendicular to velocity, so it does no work → kinetic energy stays constant; only direction changes.
- Using Ampere's law without checking symmetry; it simplifies calculations only when B is constant along the chosen loop → for irregular shapes, use Biot-Savart law.
- Mixing up the direction rules: for field from a current use right-hand grip (thumb along current), for force on a moving positive charge use right-hand palm rule (fingers along v, curl towards B, thumb gives F).
- Treating solenoid formula B = μ₀nI as valid everywhere; it applies only well inside a long solenoid → near the ends, the field is roughly half.
Quick revision
- Moving charges produce magnetic fields; stationary charges do not.
- Biot-Savart law is the fundamental relation; Ampere's law is its integral form useful with symmetry.
- Magnetic force on a charge is F = q(v × B); it changes direction, not speed.
- A current loop behaves like a magnetic dipole with moment M = NIA.
- Inside a solenoid, B = μ₀nI (uniform); outside, B ≈ 0.
- Cyclotron uses constant time period T = 2πm/(qB) to accelerate ions repeatedly.