The magnetic field around a solenoid

A straight wire carrying an electric current is surrounded by a magnetic field. Its lines of force are circles with the wire at their centre, and the direction of those circles depends on the direction of the current. Now imagine bending the wire into a single loop. Inside the loop, the circles made by every part of the wire point the same way, so their effects add together. Wind the wire into many loops lying side by side and the small fields of all the loops join into one strong field running through the middle of the coil. This is why a coil of wire behaves like a magnet when current flows in it, even though no iron and no magnet were used to make it.

A solenoid is usually made by wrapping insulated wire around a cylindrical object, such as a thin pipe or a marker pen, and then sliding the object out. What is left looks like a spring. The insulation matters because the turns lie touching one another. If the wire were bare, the current would jump straight across from one turn to the next instead of travelling all the way round each loop, and the coil would give almost no magnetic field. At the two ends, however, the insulation is scraped off, so that bare copper can touch the terminals of a battery and current can enter and leave the coil.

A home-made solenoid can be tested with a magnetic compass. The coil is connected to a 9 V battery through a battery connector, and a compass is placed beside one end of the coil.

The needle of a compass is itself a small magnet, and unlike poles attract each other. So when the current is switched on, watch which end of the needle swings towards the coil. If the south pole of the needle is pulled towards the right-hand end of the coil, then that end of the coil must be a north pole. The left-hand end must then be a south pole, and a compass placed there will have its north pole pulled in. Now swap the connections to the battery so that the current flows the other way round the coil. The needle now turns the other way: the end that was north has become south. Reversing the current reverses the poles.

The magnetic field outside a current-carrying solenoid has the same shape as the field around a bar magnet. Lines of force come out of one end, curve round the outside of the coil and go back in at the other end. Outside the coil, the field is strong at both ends and weak beside the middle portion. Inside the coil the lines run straight and parallel, evenly spaced from one end to the other, so the field inside is uniform: it has the same strength and the same direction everywhere. One end of the solenoid behaves as a North Pole and the other as a South Pole, and if the current flows in the opposite direction, the two poles change places.

A compass tells you which end is north after the circuit is built. A simple rule tells you before you even switch on, as long as you know which way the current goes round the turns.

• Use your right hand, never your left.
• Curl your fingers around the solenoid so that they follow the direction of the current in the turns.
• Stretch your thumb out along the length of the solenoid.
• The end your thumb points to is the north pole. The other end is the south pole.

Try it on an example. A solenoid lies across a table. When you curl the fingers of your right hand around it in the direction the current flows, your thumb points to the left. So the left end is the north pole and the right end is the south pole. Now turn the battery round. The current runs the other way round every turn, your fingers must curl the other way, and your thumb now points to the right. The right end has become the north pole, which is exactly what the compass showed when the battery was swapped.

The strength of the magnetic field around a solenoid depends on three things.

• (a) The magnitude of the current in the solenoid. A larger current gives a stronger field, and a smaller current a weaker one.
• (b) The number of turns in the coil. Each turn adds its own small field, so a coil with more turns gives a stronger field.
• (c) The material placed inside the solenoid, called its core. A soft iron cylinder slid inside becomes magnetised by the coil, and its own field adds to the coil's field, making it much stronger.

The field of a solenoid is temporary. It is there while current flows and it disappears when the current stops. This is exactly what makes a solenoid useful for building an electromagnet. A soft iron core is used because soft iron loses its magnetism as soon as the current is switched off, so the magnet really does turn off.

Because it can be switched on and off, and made stronger or weaker by changing the current, an electromagnet can do jobs a permanent magnet cannot. A crane in a scrapyard lifts a heap of iron with an electromagnet and drops it by switching the current off. An electric bell uses a small electromagnet to pull its hammer towards the gong again and again.

Every source of magnetism is surrounded by lines of force, but the shape of those lines depends on the source. Around a straight wire they are circles. Around a single loop they bunch together through the middle of the loop. Around a solenoid and around a bar magnet they run from one end to the other. Around the Earth they spread out from near one geographic pole and return near the other, as if a huge bar magnet lay inside the planet. Place any object in one of these fields and the number of lines passing through it depends on where it is put.

To judge how strongly a magnet acts at different places, you can simply count how many lines of force pass through the surface of an object placed there. That count has its own name.

Magnetic flux is written with the Greek letter \( \Phi \), read as phi. Its unit is the weber, written Wb.

The density of the lines of force, meaning how closely they are packed together, shows the size of the magnetic flux. Where the lines are crowded, the flux is strong. Where they are spread far apart, the flux is weak. Picture holding a small card near one pole of a bar magnet: many lines pass through it. Slide the same card along to beside the middle of the magnet and far fewer lines cross it. So the flux of a bar magnet is stronger at the poles than in the middle portion. The same reading works for a solenoid. Its lines crowd together at both ends, and inside the coil they are evenly spaced, which is another way of saying that the field inside is uniform.