define magnetic flux density as the force acting per unit current per unit length on a wire placed at right- angles to the magnetic field

Force on a Current‑Carrying Conductor

What is Magnetic Flux Density?

Imagine a wire as a tiny train track. When an electric current (I) flows through it and the track is placed in a magnetic field (B) that is at a right angle to the track, the train feels a push.

The magnetic flux density is a measure of how strong that push is per unit current and per unit length of the wire.

It is written in LaTeX as \$B\$ and measured in Tesla (T).

The relationship is:

\$B = \frac{F}{I\,L}\$

Where:

  • \$F\$ = force on the wire (in Newtons, N)

  • \$I\$ = current (in Amperes, A)

  • \$L\$ = length of wire in the field (in metres, m)

Quick Example 🚂

A 2 m long wire carries a current of 5 A in a magnetic field of 0.3 T.

Using the formula:

\$F = B\,I\,L = 0.3\,\text{T} \times 5\,\text{A} \times 2\,\text{m} = 3\,\text{N}\$

So the wire feels a 3‑Newton push perpendicular to both the current and the magnetic field.

Direction of the Force 🔄

Use the Right‑Hand Rule:

  1. Point your thumb in the direction of the current (I).

  2. Point your fingers in the direction of the magnetic field (B).

  3. The force (F) is in the direction your palm pushes.

Units & Conversion 📐

SymbolMeaningUnit
\$B\$Magnetic flux densityTesla (T) = N /(A m)
\$I\$Electric currentAmpere (A)
\$L\$Length of wire in fieldmetre (m)
\$F\$Force on wireNewton (N)

Exam Tips for A‑Level Physics

  • Always check that the wire, current and magnetic field are at right angles before applying the formula.

  • Remember the direction of the force using the right‑hand rule.

  • Use the correct units and convert if necessary (e.g., mT to T).

  • Show all steps in your calculation – examiners look for clear reasoning.

  • Practice sketching the setup: wire, field lines, and force arrow.