State that the direction of a magnetic field at a point is the direction of the force on the N pole of a magnet at that point

4.1 Simple Phenomena of Magnetism

Key Concept

The direction of a magnetic field at a point is the direction of the force on the north pole of a magnet placed at that point.

In symbols: if a north pole is placed at point P, the magnetic field vector at P, \$\vec{B}\$, points in the same direction as the force \$\vec{F}_N\$ on that north pole.

Why This Matters

When you see a magnetic field arrow in a diagram, think of it as the direction a north pole would be pushed. This simple rule helps you:

  • Predict the motion of a magnet in a field.

  • Determine the force on a moving charge: \$\vec{F}=q\,\vec{v}\times\vec{B}\$.

  • Understand the behaviour of current-carrying wires in magnetic fields.

Analogy: The Compass Needle

⚡️ A compass needle is a tiny magnet. Its north pole always points in the direction of the Earth's magnetic field. So, the field arrow you see on a map is exactly the direction a north pole would feel a force.

Examples in Everyday Life

SituationField DirectionForce on N Pole
A bar magnet near a free iron nailFrom north to south of the bar magnetNorth pole of nail is pushed away from the bar magnet’s north pole
A current‑carrying wire in a uniform fieldPerpendicular to the wire, given by right‑hand ruleForce on the wire is in the direction of the field arrow (for a north pole of a tiny magnet attached to the wire)

Exam Tip Box

🔍 Remember: The magnetic field direction is defined by the force on a north pole. When you see a field arrow, treat it as the direction a north pole would be pushed. This helps you answer questions about forces on moving charges, current loops, and magnetic dipoles.

🧲 Practice: Draw a small north pole at the point of interest and sketch the force arrow. If the force arrow matches the field arrow, you’ve got it right.

Quick Check

  1. Place a small bar magnet near a free iron nail. Which end of the nail is attracted? (Answer: the end that becomes a north pole, moving towards the magnet’s south pole.)

  2. In a uniform magnetic field pointing east, a north pole of a tiny magnet is placed at point P. In which direction does the magnetic field arrow point? (Answer: east.)

  3. When a positive charge moves northward in a magnetic field pointing east, what is the direction of the magnetic force? (Use right‑hand rule: \$\vec{F}=q\,\vec{v}\times\vec{B}\$ → force points up.)