Magnetic Fields

Finding field patterns and the force F = BIl on current-carrying wires.

  • Define and explain Magnetic Fields in your own words
  • Use key terms such as field accurately
  • Apply what you have learned to new examples and questions
  • Avoid the common mistakes learners make with this topic

This lesson focuses on Magnetic Fields: finding field patterns and the force F = BIl on current-carrying wires.

Definition: Magnetic Fields

Finding field patterns and the force F = BIl on current-carrying wires.

Key ideas

Moving charges feel magnetic forces

A current-carrying wire in a magnetic field feels F = BIl when perpendicular to the field. Fleming's left-hand rule gives the direction: First finger field, seCond finger current, thuMb motion. Charged particles curve in magnetic fields — the principle behind cyclotrons, mass spectrometers and the aurora.

Fields are mapped with lines

Field lines show direction — the way a test mass or positive charge would be pushed — and spacing shows strength: closer lines mean a stronger field. Gravitational and electric field lines radiate from masses and charges; magnetic field lines form closed loops, emerging from north poles and entering south poles.

Key term — field: A region where an object experiences a non-contact force, mapped by field lines.

Worked example: Magnetic Fields

Use Fleming's left-hand rule: magnetic field into the page, current to the right. Which way is the force?

Upwards — with the first finger pointing into the page and the second finger to the right, the thumb points up.

Answer: Upwards — with the first finger pointing into the page and the second finger to the right, the thumb points up.

Common mistakes
  • Drawing field lines crossing Field lines never cross — a crossing would mean two field directions at one point, which is impossible.
  • Confusing electric potential with field strength Potential (V) is energy per unit charge; field strength (V/m) is its gradient — E = −ΔV/Δx.

Practice

A 0.3 m wire carrying 2 A sits perpendicular to a 0.5 T field. Find the force on it.
F = BIl.

0.5 × 2 × 0.3 = 0.3 N.

Describe the electric field pattern around an isolated positive point charge.
Which way would a positive test charge be pushed?

Radial lines pointing straight outwards from the charge, getting further apart with distance as the field weakens.

Earth's mass is 6.0 × 10²⁴ kg. Calculate g at 6.4 × 10⁶ m from its centre (G = 6.67 × 10⁻¹¹ N m²/kg²).
g = GM/r².

(6.67 × 10⁻¹¹ × 6.0 × 10²⁴) ÷ (6.4 × 10⁶)² = 4.0 × 10¹⁴ ÷ 4.096 × 10¹³ ≈ 9.8 N/kg.

Why is no work done moving a charge along an equipotential?
What is the potential difference along it?

Potential is constant along an equipotential, so ΔV = 0 and W = QΔV = 0.

Quick check

Magnetic Fields — quick check

Which of these best defines "field"?

A region where an object experiences a non-contact force, mapped by field lines.

A satellite orbits at twice Earth's radius from the centre. How does g there compare to the surface value?

g ∝ 1/r², so doubling r quarters g — about 9.8 ÷ 4 ≈ 2.45 N/kg.
Key takeaways
  • Magnetic Fields: finding field patterns and the force F = BIl on current-carrying wires.
  • Moving charges feel magnetic forces: A current-carrying wire in a magnetic field feels F = BIl when perpendicular to the field.
  • field strength: Force per unit mass (N/kg) or per unit charge (N/C) at a point in the field.
  • Watch out for: drawing field lines crossing