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Moving Charges and Magnetism Class 12 Formula Sheet 2026-27

Moving Charges and Magnetism Class 12 Formula Sheet 2026-27
CBSE Class 12 PhysicsChapter 42026–27

Moving Charges and Magnetism — Formula Sheet + Quick Revision

A last-minute revision resource for formulas, definitions, directions, standard results, galvanometer conversions and common exam traps.

2026–27 syllabus boundary: Chapter 4 is part of Unit III, “Magnetic Effects of Current and Magnetism”, which carries 17 marks collectively with Chapter 5. The official syllabus includes magnetic field, Oersted’s experiment, Biot–Savart law for a circular loop, Ampere’s law for an infinitely long straight wire, force on moving charges, force on current-carrying conductors, force between parallel conductors, torque on a current loop, magnetic dipole moment and moving-coil galvanometer applications. Straight solenoid is specified as qualitative treatment only. Cyclotron is not listed in the current Chapter 4 syllabus and is therefore not included in this revision sheet.

How to revise this chapter in 20–30 minutes

  1. Read the formula table once without solving anything.
  2. Memorise the direction rules: right-hand thumb rule, Fleming’s left-hand rule and the force direction from v × B.
  3. Revise the galvanometer conversions carefully.
  4. Use the “Do not confuse” table before attempting numericals.
  5. Finish with the 60-second self-check at the end.

1. Magnetic Force on a Moving Charge

Magnetic part of Lorentz force

F = |q|vB sinθ

θ is the angle between v and B. Force is maximum at 90° and zero at 0° or 180°.

F⃗ = q(v⃗ × B⃗)

The magnetic force is perpendicular to both v and B. When magnetic force is the only force, it changes direction rather than speed.

Charged particle entering B perpendicular to velocity

qvB = mv²/r
r = mv/(|q|B)
ω = |q|B/m
T = 2πm/(|q|B)

Exam insight: for a fixed particle, r ∝ v/B, while T is independent of speed for perpendicular circular motion in uniform B.

Velocity selector condition

qE = qvB  ⇒  v = E/B

For no deflection, electric and magnetic forces must be equal and opposite in the stated geometry.

2. Magnetic Field Due to Current

Biot–Savart law

dB⃗ = (μ₀/4π) [I(dℓ⃗ × r̂)/r²]

For Chapter 4, the key standard result used numerically is the field at the centre of a circular current-carrying loop.

Field at the centre of a circular coil

B = μ₀NI/(2R)

N = number of turns, I = current and R = radius.

Long straight current-carrying conductor

B = μ₀I/(2πr)

r is the perpendicular distance from the wire; B decreases as 1/r.

μ₀ = 4π × 10⁻⁷ T m A⁻¹

3. Ampere’s Law

Integral form

∮ B⃗ · dℓ⃗ = μ₀Ienclosed

For an infinitely long straight wire, the symmetric result is B = μ₀I/(2πr).

Syllabus trap: The 2026–27 syllabus says “Straight solenoid (only qualitative treatment).” Do not turn solenoid into a detailed numerical section on this revision page.

4. Force on a Current-Carrying Conductor

Force on a straight conductor in uniform B

F = BIL sinθ

θ is the angle between current direction and B. Maximum force: 90°. Zero force: conductor parallel to B.

Force between two parallel current-carrying conductors

F/L = μ₀I₁I₂/(2πd)

d is the separation between the conductors.

Current directionsForce
Same directionAttractive
Opposite directionsRepulsive

5. Torque and Magnetic Dipole Moment

Magnetic dipole moment

m = NIA

Direction of m is perpendicular to the plane of the loop, given by the right-hand rule.

Torque on a current loop

τ = NIAB sinθ
τ = mB sinθ

θ is the angle between m and B. Maximum torque = mB at 90°; torque is zero at 0° or 180°.

Zero torque

τ = 0 when θ = 0° or 180°.

Maximum torque

τmax = mB when θ = 90°.

6. Moving-Coil Galvanometer

Basic working relation

τmagnetic = NIAB
τrestoring = kθ
NIAB = kθ
θ/I = NBA/k

At equilibrium, magnetic torque balances restoring torque. In the radial-field arrangement, the effective torque factor is unity.

Current sensitivity

θ/I = NBA/k

More turns, larger area and stronger B increase current sensitivity; larger k decreases it.

Voltage sensitivity

θ/V = NBA/(kG)

G is the galvanometer resistance.

7. Galvanometer → Ammeter

Shunt resistance

S = IgG/(I − Ig)

I = desired ammeter range, Ig = full-scale galvanometer current, G = galvanometer resistance.

ConnectionPurpose
Shunt S in parallelProvides a low-resistance path for most of the larger current.

8. Galvanometer → Voltmeter

Series resistance

R = V/Ig − G

V = desired voltmeter range. The external resistance is connected in series.

ConnectionPurpose
Large resistance R in seriesLimits current through the galvanometer for voltage measurement.

9. Direction Rules — Must Know

SituationRule / direction
Field around a straight current-carrying wireRight-hand thumb rule: thumb → current; curled fingers → magnetic field.
Force on current-carrying conductorFleming’s left-hand rule gives the force direction from field and current.
Force on a positive chargeDirection of v × B.
Force on a negative chargeOpposite to v × B.
Magnetic moment of a current loopRight-hand rule: curled fingers follow current; thumb gives m direction.

10. The “Do Not Confuse” Table

Do not confuseCorrect distinction
q vs |q| in force magnitudeUse |q| for magnitude; charge sign affects direction.
R vs rR commonly denotes coil radius; r commonly denotes distance from a straight wire or particle-path radius depending on context.
Ammeter conversionLow-resistance shunt is connected in parallel.
Voltmeter conversionHigh series resistance is connected in series.
θ in F = BIL sinθAngle is between current direction and B.
θ in τ = mB sinθAngle is between m and B.
Same parallel currentsAttract.
Opposite parallel currentsRepel.

11. One-Minute Unit Check

QuantitySI unit
Magnetic field Btesla (T) = N A⁻¹ m⁻¹
Magnetic dipole moment mA m²
Torque τN m
Current sensitivity θ/Irad A⁻¹
Charge qcoulomb (C)
Magnetic force Fnewton (N)

12. 60-Second Self-Check

  1. Can you write F = qvB sinθ and identify when it is zero?
  2. Can you obtain r = mv/(|q|B) for perpendicular motion?
  3. Can you write the field at the centre of an N-turn circular coil?
  4. Can you state B ∝ I/r for a long straight wire?
  5. Can you state attraction/repulsion for parallel currents?
  6. Can you write m = NIA and τ = mB sinθ?
  7. Can you write the shunt formula for an ammeter?
  8. Can you write the series-resistance formula for a voltmeter?
  9. Can you state the direction of force on a negative charge?
  10. Can you explain why a magnetic force alone does no work on a moving charge?

13. Last-Minute Revision Strategy

Before the exam: formula bank → direction rules → galvanometer conversions → three standard field results → torque/dipole relations → one or two solved numericals. Avoid spending final revision time on older, out-of-scope extensions.

Research note: This page follows the official CBSE Class XII Physics 2026–27 curriculum. Chapter 4 and Chapter 5 together form Unit III, carrying 17 theory marks. The current syllabus specifies straight solenoid as qualitative treatment only. The current CBSE Class XII 2026–27 SQP/MS portal is the official sample-paper reference. This is a revision resource, not an official CBSE document.

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