← Magnets and magnetic fields; electromagnets

What the field-line direction means

A plotting compass sits on a field line near a bar magnet. Which way does its north end point?

Every field diagram you have drawn carries arrowheads. Outside the magnet, the arrows run from the N end to the S end. But what is one arrowhead saying, at one spot?

SNWHAT DOES THE ARROWHEAD MEAN?
A bar magnet and its field lines. Every line carries an arrowhead.

In the Fields topic, field lines came with a reading: a line's direction shows the direction of the force the field would exert. And you have just seen the compass clue: a needle's north end settles pointing the way the arrow points.

Imagine a magnetic pole you could carry on its own: a single north pole, with nothing attached. No such lone pole exists to buy. But it is the standard test object for a magnetic field, like the test mass and the positive test charge from the Fields topic. We call it a free north pole.

SNFORCEFREE NORTH POLE
A free north pole on a field line above the magnet. The force on it points the way the arrow points, toward the magnet's S end.

Place the free north pole at a point above the magnet. At that point, the line runs from the N end toward the S end. The field exerts a force on the free north pole in exactly that direction, toward the S end.

SNFORCEFREE NORTH POLE
The same free north pole, now just beyond the N end. The force follows the arrow again, away from the magnet.

Now the free north pole sits just beyond the magnet's N end. There, the line's arrow points away from the magnet. The force on the free north pole points that way too, along the line and away from the magnet.

The direction of a magnetic field line shows the direction of the force on a free north pole placed there.

A compass needle's north end behaves almost like a free north pole. The force on its north end points the way the arrow points, so the needle swings into line.

What does the direction of a magnetic field line show?

A free north pole sits on a field line. Which way is it pushed?

This completes a family you already know. A test mass reads a gravitational field. A positive test charge reads an electric field. A free north pole reads a magnetic field.

FIELDITS TEST OBJECTA gravitational fielda test massAn electric fielda positive test chargeA magnetic fielda free north pole
Each kind of field has its own test object.

Petra says a field line's arrow shows the push a free north pole would feel there. Is Petra correct?

A free north pole is placed above the middle of a bar magnet, where the field line runs from the N end toward the S end. Which way does the force on it point?

The field line's direction shows the force direction on a free north pole.

The line at this point runs toward the magnet's S end.

The force on the free north pole points along the line, toward the magnet's S end.

At a spot on a field diagram, the field line points straight north. A free north pole is placed there. What is the direction of the force on it?

The line's direction shows the force direction on a free north pole.

The line points north.

The force on the free north pole points north.

Your turn

A free north pole sits at the dot below the magnet. Which way is it pushed?

SNFREE NORTH POLE

Which test object defines the direction of a magnetic field line?

At a spot beside a magnet, the force on a free north pole points west. Which way does the field line at that spot point?