Moving Charges and Magnetism Class 12 Formula Sheet 2026-27
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.
How to revise this chapter in 20–30 minutes
- Read the formula table once without solving anything.
- Memorise the direction rules: right-hand thumb rule, Fleming’s left-hand rule and the force direction from v × B.
- Revise the galvanometer conversions carefully.
- Use the “Do not confuse” table before attempting numericals.
- Finish with the 60-second self-check at the end.
1. Magnetic Force on a Moving Charge
Magnetic part of Lorentz force
θ is the angle between v and B. Force is maximum at 90° and zero at 0° or 180°.
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
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
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
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
N = number of turns, I = current and R = radius.
Long straight current-carrying conductor
r is the perpendicular distance from the wire; B decreases as 1/r.
3. Ampere’s Law
Integral form
For an infinitely long straight wire, the symmetric result is B = μ₀I/(2πr).
4. Force on a Current-Carrying Conductor
Force on a straight conductor in uniform B
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
d is the separation between the conductors.
| Current directions | Force |
|---|---|
| Same direction | Attractive |
| Opposite directions | Repulsive |
5. Torque and Magnetic Dipole Moment
Magnetic dipole moment
Direction of m is perpendicular to the plane of the loop, given by the right-hand rule.
Torque on a current loop
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
At equilibrium, magnetic torque balances restoring torque. In the radial-field arrangement, the effective torque factor is unity.
Current sensitivity
More turns, larger area and stronger B increase current sensitivity; larger k decreases it.
Voltage sensitivity
G is the galvanometer resistance.
7. Galvanometer → Ammeter
Shunt resistance
I = desired ammeter range, Ig = full-scale galvanometer current, G = galvanometer resistance.
| Connection | Purpose |
|---|---|
| Shunt S in parallel | Provides a low-resistance path for most of the larger current. |
8. Galvanometer → Voltmeter
Series resistance
V = desired voltmeter range. The external resistance is connected in series.
| Connection | Purpose |
|---|---|
| Large resistance R in series | Limits current through the galvanometer for voltage measurement. |
9. Direction Rules — Must Know
| Situation | Rule / direction |
|---|---|
| Field around a straight current-carrying wire | Right-hand thumb rule: thumb → current; curled fingers → magnetic field. |
| Force on current-carrying conductor | Fleming’s left-hand rule gives the force direction from field and current. |
| Force on a positive charge | Direction of v × B. |
| Force on a negative charge | Opposite to v × B. |
| Magnetic moment of a current loop | Right-hand rule: curled fingers follow current; thumb gives m direction. |
10. The “Do Not Confuse” Table
| Do not confuse | Correct distinction |
|---|---|
| q vs |q| in force magnitude | Use |q| for magnitude; charge sign affects direction. |
| R vs r | R commonly denotes coil radius; r commonly denotes distance from a straight wire or particle-path radius depending on context. |
| Ammeter conversion | Low-resistance shunt is connected in parallel. |
| Voltmeter conversion | High series resistance is connected in series. |
| θ in F = BIL sinθ | Angle is between current direction and B. |
| θ in τ = mB sinθ | Angle is between m and B. |
| Same parallel currents | Attract. |
| Opposite parallel currents | Repel. |
11. One-Minute Unit Check
| Quantity | SI unit |
|---|---|
| Magnetic field B | tesla (T) = N A⁻¹ m⁻¹ |
| Magnetic dipole moment m | A m² |
| Torque τ | N m |
| Current sensitivity θ/I | rad A⁻¹ |
| Charge q | coulomb (C) |
| Magnetic force F | newton (N) |
12. 60-Second Self-Check
- Can you write F = qvB sinθ and identify when it is zero?
- Can you obtain r = mv/(|q|B) for perpendicular motion?
- Can you write the field at the centre of an N-turn circular coil?
- Can you state B ∝ I/r for a long straight wire?
- Can you state attraction/repulsion for parallel currents?
- Can you write m = NIA and τ = mB sinθ?
- Can you write the shunt formula for an ammeter?
- Can you write the series-resistance formula for a voltmeter?
- Can you state the direction of force on a negative charge?
- 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.
Continue Chapter 4 Preparation
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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