Magnetic force and magnetic fields, explained

By Ashraf Bhura, Co-Founder, STEM-Tutor · Updated October 2026

Magnetic fields push on moving charges and on wires carrying current. That force drives electric motors, steers particles in accelerators and protects the Earth from the solar wind. This guide covers the magnetic force at AP, A level and GCSE level.

Magnetic fields

A magnetic field is a region where a magnet, a magnetic material or a moving charge feels a force. Field lines show its direction: they point from north to south outside a magnet, and the closer together they are, the stronger the field. The strength of a magnetic field is measured by the magnetic flux density B, in tesla (T). The Earth's field is about 5 × 10⁻⁵ T; a strong fridge magnet is around 0.01 T; an MRI scanner is 1.5 to 3 T.

Electric currents create magnetic fields. A straight wire produces circular field lines around it, and a coil of wire (a solenoid) produces a field like a bar magnet's, which is the basis of an electromagnet.

Force on a moving charge

F = q v B sinθ

q is the charge, v its speed, B the field strength and θ the angle between the velocity and the field. Three key facts follow:

• A stationary charge feels no magnetic force.
• A charge moving parallel to the field (θ = 0) feels no force.
• The force is greatest when the charge moves perpendicular to the field, and it always acts at right angles to both the velocity and the field.

Because the force is always perpendicular to the velocity, it does no work. A magnetic field can change the direction of a charged particle, but never its speed.

Finding the direction

In the US, the right-hand rule is common: point your fingers along v, curl them towards B, and your thumb gives the force on a positive charge. For a negative charge, such as an electron, the force is in the opposite direction. In the UK, Fleming's left-hand rule is used for current-carrying wires: First finger along the Field, seCond finger along the Current (conventional, positive to negative), and thuMb gives the Motion (force). Both rules give the same answers.

Force on a current-carrying wire

F = B I L sinθ

I is the current, L the length of wire in the field and θ the angle between the wire and the field. This is the motor effect. At GCSE, with the wire at right angles to the field, it is written F = BIL.

Worked examples

Example 1: force on a wire

A 0.25 m wire carries 4.0 A at right angles to a 0.30 T field. Find the force.

• F = BIL = 0.30 × 4.0 × 0.25 = 0.30 N.

Example 2: an angled wire

The same wire is turned to 30° to the field. Find the new force.

• F = 0.30 × sin 30° = 0.15 N.

Example 3: force on a proton

A proton moves at 2.0 × 10⁶ m/s perpendicular to a 0.50 T field. Find the force. (e = 1.6 × 10⁻¹⁹ C)

• F = qvB = 1.6 × 10⁻¹⁹ × 2.0 × 10⁶ × 0.50.
• F = 1.6 × 10⁻¹³ N.

Circular motion of charged particles

When a charged particle moves perpendicular to a uniform field, the magnetic force is always at right angles to its velocity, so it acts as a centripetal force and the particle moves in a circle. Setting qvB = mv²/r gives the radius:

r = mv / (qB)

Faster or heavier particles move in bigger circles; stronger fields or larger charges make tighter circles. This is the principle behind mass spectrometers, which separate isotopes by their different radii, and cyclotrons, which accelerate particles.

Example 4: radius of a path

An electron moving at 3.0 × 10⁷ m/s enters a 2.0 × 10⁻³ T field at right angles. Find the radius of its path. (m_e = 9.11 × 10⁻³¹ kg)

• r = mv/(qB) = (9.11 × 10⁻³¹ × 3.0 × 10⁷)/(1.6 × 10⁻¹⁹ × 2.0 × 10⁻³).
• r ≈ 0.085 m, about 8.5 cm.

Example 5: a velocity selector

In a region with an electric field E = 4.0 × 10⁴ V/m and a perpendicular magnetic field B = 0.020 T, which speed of ion passes straight through?

• Straight through means the electric and magnetic forces balance: qE = qvB.
• v = E/B = 4.0 × 10⁴/0.020 = 2.0 × 10⁶ m/s, for any charge.

Electric motors

A simple DC motor is a coil of wire in a magnetic field. Current flows one way along one side of the coil and the opposite way along the other, so the motor effect pushes one side up and the other down, making the coil turn. A split-ring commutator reverses the current every half turn, so the coil keeps turning in the same direction. The motor turns faster with a larger current, a stronger magnet or more turns on the coil. Loudspeakers use the same effect: a varying current in a coil makes it vibrate in a magnetic field, producing sound.

Forces between parallel wires

Two parallel wires carrying current each sit in the other's magnetic field, so they exert forces on each other. Currents in the same direction attract; currents in opposite directions repel. This is covered in AP Physics C and A level Physics, and it was historically used to define the ampere.

Common mistakes

• Applying a magnetic force to a stationary charge, or to one moving parallel to the field.
• Forgetting to reverse the direction for negative charges such as electrons.
• Using electron flow instead of conventional current in Fleming's left-hand rule.
• Thinking a magnetic field speeds up a charged particle; it only changes its direction.

Practice questions

Try each one before opening the answer.

Frequently asked questions

Is magnetic force on the AP Physics exams?

Yes. Magnetic forces on charges and wires are in AP Physics 2 and AP Physics C: Electricity and Magnetism in the current course framework.

Is this in GCSE and A level Physics?

GCSE covers magnetic fields, electromagnets and the motor effect with F = BIL (Higher). A level adds F = BQv, circular paths of charged particles and applications such as mass spectrometers.

Key takeaways

• Magnetic field lines run from north to south; B is measured in tesla.
• On a charge: F = qvB sinθ; on a wire: F = BIL sinθ.
• The force is perpendicular to both motion and field, so it does no work.
• Charged particles in a uniform field move in circles: r = mv/(qB).
• Motors use the motor effect with a commutator to keep turning.

Related guides

• Faraday's law
• Centripetal force
• Coulomb's law