Reading the Invisible Map Around a Wire

Place a straight copper wire so it runs directly over a small compass, connect the wire into a circuit with a cell and a key, and close the key. The compass needle swings away from its resting direction the instant current begins to flow, exactly the same deflection Hans Christian Oersted stumbled onto by accident in 1820, and exactly the same effect explored in an earlier chapter with a coil-wrapped nail lifting paper clips. Confirming this same link twice, with two different setups, is not repetition for its own sake; it sets up the real question this chapter is built around. If a current-carrying wire genuinely produces a magnetic field, what does that field actually look like, in detail, and can its exact shape be mapped out, the same way a bar magnet's field can be? Answering that question precisely is what everything else in this chapter builds toward.

Scatter iron filings evenly around a bar magnet resting on paper, tap the paper gently, and the filings settle into a distinctive, repeatable pattern, curving from one end of the magnet around to the other. This region surrounding a magnet, where its force can genuinely be detected, is what defines a magnetic field, and the curved paths the filings trace out represent magnetic field lines. A second, more deliberate way to draw the same lines uses a compass instead of filings: placed near the magnet's North pole and traced step by step, always moving the compass so its previous position lines up correctly, the path a compass needle traces out forms a smooth curve, one complete field line, and repeating this from different starting points builds up the full pattern. Three consistent rules govern every field-line diagram, for any magnet. Outside the magnet, field lines run from North pole to South pole, by definition, since a field's direction at any point is fixed as the direction a compass's own North pole would point there. Field lines are closed curves, continuing through the inside of the magnet from South back to North, and closing the loop. And no two field lines ever cross, since a crossing point would mean a compass placed exactly there would have to point in two directions simultaneously, which is simply not possible.

Pass a long, thick, straight copper wire vertically through a hole in a horizontal piece of cardboard, connect it in series with a battery and a rheostat, sprinkle iron filings evenly across the cardboard, and tap it gently once current flows. The filings arrange themselves into a strikingly clean pattern: a series of complete circles, all centred exactly on the wire itself. Placing a compass at different points on any one of these circles, and noting the direction its North pole points each time, shows that the circles themselves are the field lines, direction included, produced by the current. Two further checks reveal how this field actually behaves. Reversing the current's direction through the wire reverses the direction every needle points, meaning the field lines' direction flips too. And varying the current or the distance from the wire changes the compass's deflection: a larger current produces a stronger deflection at the same point, while moving the compass further from the wire, at the same current, produces a weaker one, matching how the concentric circles themselves grow larger, and further apart, moving outward from the wire. There is a clean, memorable way to find this field's direction without needing filings or a compass at all: imagine gripping the current-carrying wire in your right hand, thumb pointing in the direction of the current, and your curled fingers show the direction the field lines circle in, a technique called the right-hand thumb rule, also known as Maxwell's corkscrew rule, since it matches the direction an ordinary corkscrew turns when driven forward.

Bend that same straight current-carrying wire into a circular loop, and the concentric-circle pattern does not vanish, it simply transforms. Near the wire itself, the field lines still curve as circles; but moving inward, toward the centre of the loop, those circles grow larger and larger, until at the exact centre, small enough arcs from every part of the loop combine to look like straight lines. Since current in every part of a circular loop flows the same overall way around, each part's contribution to the field at the centre adds up in the same direction, so a coil with several turns produces a field that many times stronger than one turn alone, directly proportional to the number of turns. Wind that same wire into a long, tightly packed cylindrical coil of many turns instead of just one loop, and the result is called a solenoid, and its field pattern is genuinely striking: viewed from outside, it looks essentially identical to a bar magnet's own field, with one end behaving as a North pole and the other as a South pole, while the field lines running through the solenoid's interior are straight and evenly spaced, meaning the field inside is uniform, the same strength at every point inside the coil. Placing a piece of soft iron inside a current-carrying solenoid puts this strong, uniform internal field to direct use: the iron becomes strongly magnetised for as long as current flows, an electromagnet, the exact device already built earlier in this thread with nothing more than a coiled wire, a cell, and an iron nail.

So far, current has been the cause and a magnetic field the effect. The French scientist Andre-Marie Ampere suggested the reverse should also be true, that a magnetic field ought to exert an equal and opposite force back on the current-carrying conductor sitting inside it. Suspend a light aluminium rod horizontally between the poles of a strong horseshoe magnet, oriented so the magnetic field points straight upward, then pass a current through the rod: it visibly swings sideways, displaced by a real, measurable force. Reverse the current's direction through the same rod, and the displacement reverses too, now swinging the opposite way. Reverse the magnetic field's direction instead, by swapping the magnet's poles, keeping the current the same as before, and the displacement reverses yet again. The force is at its largest when current and field are exactly perpendicular to each other, and in that specific, most common case, there is a clean way to predict the force's direction: stretch the thumb, first finger and middle finger of your left hand so all three are mutually perpendicular, point the first finger along the magnetic field and the second finger along the current, and the thumb then points in the exact direction of the force, a technique called Fleming's left-hand rule. This single push-back effect, a magnetic field exerting a mechanical force on a current, is the working principle behind an entire family of everyday devices: electric motors, loudspeakers, microphones, and various measuring instruments all rely on it directly.

Every electric current produces a magnetic field, without exception, which raises a genuinely surprising thought: your own body runs on tiny electric currents constantly, so does it produce a magnetic field too? It does. Every time a nerve carries an electrical impulse, telling a muscle to move when you touch something, that impulse briefly produces a magnetic field of its own, though an extremely faint one, roughly a billion times weaker than the Earth's own magnetic field. Two organs produce a magnetic signal strong enough to matter practically: the heart and the brain. This is not just a curiosity; it is the physical basis of a genuinely important medical imaging technique, Magnetic Resonance Imaging, or MRI, which analyses the body's own internal magnetic fields to build detailed images of internal organs and tissues, without needing surgery or the ionising radiation an X-ray uses. A chapter that began with a compass needle twitching next to a copper wire ends, by exactly the same underlying physics, inside a hospital imaging suite, mapping the inside of a human body.