Q1. A proton (q = 1.6×10⁻¹⁹ C) moves at 2×10⁶ m/s perpendicular to a 0.5 T field. Find the force on it.
F = qvB sin90°
F = 1.6×10⁻¹⁹ × 2×10⁶ × 0.5
F = 1.6×10⁻¹³ N
Moving Charges and Magnetism — Class 12
Magnetism is electricity in motion. Compute the force on a current-carrying wire and on a moving charge, then practise the formulas examiners reuse every year.
Force on a moving chargeF = qvB sinθ. The force is perpendicular to both v and B, so a charged particle moves in a circle in a uniform field.
Force on a conductorA current-carrying wire in a field feels F = BIL sinθ. Direction from Fleming's left-hand rule — the basis of the electric motor.
Biot–Savart & Ampère's lawUsed to find the magnetic field of currents. For a long solenoid the inside field is B = μ₀nI (n = turns per metre).
Radius of circular pathA charge of mass m moving perpendicular to B follows a circle of radius r = mv/qB (used in the cyclotron).
Magnetic force calculator Interactive
Find the force on a current-carrying wire placed perpendicular to a magnetic field (F = BIL).
Force, F = B·I·L—N
The force is greatest when the wire is perpendicular to the field (θ = 90°) and zero when it is parallel.
Numericals practice Interactive
Force-on-a-conductor and field problems with worked steps.
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Solved numericals
Q2. A solenoid has 1000 turns per metre and carries 2 A. Find the magnetic field inside (μ₀ = 4π×10⁻⁷).
B = μ₀ n I
B = 4π×10⁻⁷ × 1000 × 2
B = 2.51×10⁻³ T
Formula sheet
| Quantity | Formula | SI unit |
|---|---|---|
| Force on a moving charge | F = q v B sinθ | newton (N) |
| Force on a conductor | F = B I L sinθ | N |
| Radius of circular path | r = m v / (q B) | m |
| Field inside a solenoid | B = μ₀ n I | tesla (T) |
| Torque on a current loop | τ = N B I A sinθ | N·m |
Common mistakes & exam wins
- The magnetic force on a charge is always perpendicular to its velocity, so it changes direction but never speed (no work done).
- Use Fleming's LEFT-hand rule for the force on a current (motor); the RIGHT-hand rule is for induced current (generator).
- F = BIL sinθ is maximum at θ = 90° and zero when the wire is parallel to the field.
- Inside a long solenoid the field B = μ₀nI is uniform and depends only on turns-per-metre and current, not the area.
Frequently asked questions
What is the force on a current-carrying conductor in a magnetic field?
F = BIL sinθ, where B is the field, I the current, L the length and θ the angle between the wire and the field; its direction is given by Fleming's left-hand rule.
Why does a charged particle move in a circle in a magnetic field?
Because the magnetic force F = qvB is always perpendicular to the velocity, it acts as a centripetal force, giving a circular path of radius r = mv/qB.
What is the magnetic field inside a solenoid?
B = μ₀nI, where n is the number of turns per metre and I the current; the field is uniform and parallel to the axis.
Does a magnetic force do work on a moving charge?
No. Because the force is always perpendicular to the velocity, it changes the direction of motion but not the speed, so it does zero work.