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A magnet with an off switch

• A scrapyard crane picks up a tonne of steel, swings it across the yard, and drops it by flicking a switch.
• No permanent magnet can do that. What the crane carries is a coil of wire around an iron core, and its magnetism exists only while the current flows.
• Every field in this lesson comes from a current, which means every one of them can be switched, reversed or made stronger at will.
• This lesson is the field patterns that currents produce, and the forces between two currents.

The field around a straight wire

• The field forms concentric circles around the wire, in the plane perpendicular to it.
• Their spacing widens with distance, because the field weakens as you move away.
• The direction comes from the right-hand grip rule 右手定则: grip the wire with your right hand, thumb along the current, and your fingers curl the way the field points.
• For a current into the page, that gives a clockwise field.

Circles, widening, each with an arrow

The flat circular coil

• Bend the wire into a loop and the circular fields around each side reinforce through the centre.
• So the field at the centre is at right angles to the plane of the coil, and strongest there.
• Seen from one face the coil behaves as a north pole, since the field leaves it there; from the other face, a south pole. A single loop is already a small bar magnet 条形磁铁.

The solenoid

• A solenoid 螺线管 is many such loops in a row. Their fields add along the axis, so inside the field is nearly uniform and parallel to the axis, exactly like a stretched bar magnet.
• Outside it spreads out and falls off fast, and the ends behave as N and S poles.
• Three things strengthen it: more turns per unit length, a larger current, and an iron core 铁芯.

Uniform down the axis, and poles at the ends

Worked example: why the core helps

Two parallel currents

• Each wire sits in the field of the other, so each experiences a motor-effect force $F = BIL$.
• Apply the left-hand rule to each wire in turn, using the field the other one makes. The result is symmetric, as Newton's third law requires.
• Currents in the same direction attract. Currents in opposite directions repel.
• This force is the basis of the historical definition of the ampere.

Worked example: predicting the direction

Marks that slip away

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