recall and use the equation F = BIL sin θ, with directions as interpreted by Fleming’s left-hand rule

Key Equation

When a straight conductor of length L carries a current I in a magnetic field B, the magnetic force is given by

\$F = B\,I\,L\,\sin\theta\$

where θ is the angle between the direction of the magnetic field and the direction of the current.

Understanding the Variables

• B – Magnetic field strength (Tesla, T)
• I – Electric current (Amperes, A)
• L – Length of conductor in the field (metres, m)
• θ – Angle between B and I (degrees or radians)
• Resulting force F is measured in Newtons (N)

Fleming’s Left‑Hand Rule 🧲

Use your left hand to find the direction of the force:

1. Thumb = Force (F)
2. First finger = Magnetic field (B) – points into or out of the page
3. Second finger = Current (I) – points along the wire

Hold your left hand so that the first and second fingers are perpendicular. The thumb will point in the direction of the magnetic force.

Practical Example 📐

Suppose a 0.5 m long wire carries a 4 A current upward. The magnetic field is 0.3 T directed into the page. What is the magnitude and direction of the force?

1️⃣ Calculate sin θ (θ = 90° so sin θ = 1).

2️⃣ Plug into the equation:

\$F = 0.3\,\text{T} \times 4\,\text{A} \times 0.5\,\text{m} \times 1 = 0.6\,\text{N}\$

3️⃣ Direction: Using Fleming’s rule, thumb points to the right (↔️). So the wire is pushed horizontally to the right.

Exam Tips 🧠

• Always write the full equation with all symbols.
• Check units: B in T, I in A, L in m, F in N.
• Use Fleming’s left‑hand rule to state the direction of F.
• Remember that sin θ is 1 when the field and current are perpendicular.
• Show all steps in your calculation; partial credit is awarded for correct reasoning.

Quick Reference Table 📊