Recall and use the relative directions of force, magnetic field and current

Published by Patrick Mutisya · 14 days ago

IGCSE Physics 0625 – Force on a Current‑Carrying Conductor

4.5.4 Force on a Current‑Carrying Conductor

Objective

Recall and use the relative directions of the magnetic field B, the current I, and the magnetic force F on a straight conductor.

Key Concepts

  • The magnetic force on a length l of conductor carrying current I in a uniform magnetic field B is given by

    \$\mathbf{F}=I\,\mathbf{l}\times\mathbf{B}\$

  • The magnitude of the force is

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

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

  • The direction of F is found using the right‑hand rule (conventional current) or Fleming’s left‑hand rule (electron flow).

Right‑Hand Rule (Conventional Current)

To determine the direction of the magnetic force on a straight conductor:

  1. Point the thumb of your right hand in the direction of the conventional current I (from positive to negative).

  2. Stretch the fingers so they point in the direction of the magnetic field B (from north to south).

  3. The palm (or the direction your palm pushes) gives the direction of the force F on the conductor.

Suggested diagram: Right‑hand rule showing thumb (I), fingers (B), and palm (F).

Table – Relative Directions

Current Direction (I)Magnetic Field Direction (B)Resulting Force Direction (F)
Into the page (×)To the right (→)Upwards (↑)
To the right (→)Upwards (↑)Out of the page (·)
Downwards (↓)Into the page (×)To the left (←)

Using the Formula

When the conductor is perpendicular to the magnetic field (θ = 90°), the sine term becomes 1 and the equation simplifies to:

\$F = I\,l\,B\$

Example: A 0.15 m long wire carries 3.0 A in a magnetic field of 0.40 T, perpendicular to the wire. The force on the wire is:

\$F = (3.0\ \text{A})(0.15\ \text{m})(0.40\ \text{T}) = 0.18\ \text{N}\$

Common Mistakes

  • Confusing the direction of electron flow with conventional current – always use the direction of positive charge flow for the right‑hand rule.

  • Omitting the sine factor when the field is not perpendicular; remember F is maximum only at θ = 90°.

  • Mixing up the symbols: B is the magnetic field, not the magnetic flux density Φ.

Summary

To determine the magnetic force on a current‑carrying conductor:

  1. Identify the direction of the current (I) and the magnetic field (B).

  2. Apply the right‑hand rule to find the direction of the force (F).

  3. Use \$F = I\,l\,B\sin\theta\$ to calculate the magnitude, remembering that \$l\$ is the length of wire within the uniform field.

Practice Questions

  1. A straight wire of length 0.20 m carries a current of 2.5 A. It is placed in a uniform magnetic field of 0.30 T directed into the page. The current flows to the right.

    • Determine the direction of the magnetic force.

    • Calculate the magnitude of the force.

  2. A conductor of length 0.10 m carries a current of 4.0 A at an angle of 30° to a magnetic field of 0.50 T. Find the magnitude of the force.

  3. Explain why a current‑carrying loop placed in a uniform magnetic field experiences a torque but no net translational force.