Magnetic field due to a solenoid

What a solenoid is. A solenoid is a long coil of insulated wire wound closely, turn after turn, in the shape of a helix — usually around a cylindrical former, like a spring stretched out with its coils touching. Current sent through the wire flows around every turn in the same sense.

The field pattern. Sprinkle iron filings around a current-carrying solenoid and they trace field lines emerging from one end, arcing around the outside of the coil, and re-entering the other end — then continuing inside the coil back to the first end, closing the loop. This is precisely the pattern a bar magnet produces: one end behaves as an effective north pole, the other as an effective south pole.

The one thing a single loop cannot do. Look closely at the field inside the solenoid, away from its two ends. There, the field lines are straight, run parallel to the coil's axis, and are evenly spaced — meaning the field has the same strength and direction at every point in that central region. This uniform field inside is the solenoid's signature property, and it is what separates it from a single circular loop, whose field lines curve and change strength from point to point even near the centre.

Finding the poles — right-hand thumb rule. The same right-hand thumb rule that gives the field of a single loop applies turn by turn around a solenoid: curl the fingers of the right hand in the direction the current flows around the coil, and the thumb points along the axis, out of the end that behaves as the north pole.

Electromagnets. Slide a core of soft iron — a material that magnetises strongly while current flows but loses almost all its magnetism the instant the current stops — inside the solenoid, and the combination becomes an electromagnet. The soft-iron core greatly strengthens the field compared to an air-core solenoid, and because the magnetism switches off with the current, electromagnets can be turned on, turned off, and (by changing the current) made stronger or weaker on demand. This controllability is what a permanent magnet can never offer, and it is why electromagnets — not permanent magnets — run electric bells, cranes that lift and drop scrap iron, and loudspeakers.

Nothing here needs a new law — the solenoid's field is just many single-loop fields, from the earlier lesson, added together turn by turn, and the syllabus goal is to see why stacking loops produces a uniform field inside while a lone loop does not.

Step 1. Recall the field of one circular current loop: field lines pass through the loop's centre roughly straight but curve away and weaken as you move outward, and even at the centre the field is not perfectly uniform across a wide region — it is strongest exactly at the middle and falls off away from the loop's axis and plane. A single loop gives you one such "bundle" of field lines squeezed through one ring.

Step 2. Now place many identical loops side by side, all carrying current in the same sense, close enough that they nearly touch — that is exactly what a tightly wound solenoid is. Each loop contributes its own bundle of field lines through its centre, all pointing the same way along the axis (since the right-hand thumb rule gives every turn the same field direction).

Step 3. Deep inside the coil, away from the two open ends, a point on the axis sits surrounded by many turns on every side — turns just to its left and just to its right, all reinforcing the same axial field direction and largely cancelling out each other's outward curving. The individual loops' contributions overlap and add up so thoroughly that the net field settles into straight, evenly spaced lines: the uniform field inside the solenoid.

Step 4. Near the two ends, however, a point does not have turns wrapping around on both sides — it only "sees" coil on one side — so the field there behaves more like a single loop's field, spreading out and curving as it exits. This is exactly the pattern seen with iron filings: straight and uniform deep inside, but curving outward and weakening as field lines approach and leave the two ends, then arcing around the outside exactly as a bar magnet's field does.

Question: A solenoid is wound so that, viewed from its right-hand end, the current flows anticlockwise around the turns. It is then wound around a soft-iron core to make an electromagnet used to lift small iron nails. State which end of the solenoid behaves as the north pole, describe the field just inside the middle of the coil, and state two ways the electromagnet's lifting strength could be increased.

Step 1. Apply the right-hand thumb rule: curl the fingers of the right hand in the direction of current flow. Viewed from the right-hand end, the current is anticlockwise, so curling the fingers that way makes the thumb point out of that end, toward the viewer.

Step 2. Since field lines emerge from a north pole, the end the thumb points out of — the right-hand end — behaves as the north pole; the opposite end behaves as the south pole.

Step 3. Well inside the solenoid, away from the ends, the field lines run straight, parallel to the axis, and evenly spaced, pointing from the south end toward the north end — this is the uniform-field region, strengthened further by the soft-iron core magnetising along with it.

Step 4. The electromagnet's strength can be increased by increasing the current flowing through the coil, or by increasing the number of turns of wire wound onto the core; either change strengthens the magnetising effect without changing the soft-iron core itself.

Answer: the right-hand end is the north pole; inside the coil the field is straight, parallel, and uniform, running south to north; strength increases with more current or more turns.

• Confusing a solenoid's field with a single loop's field — the solenoid's signature feature is the uniform field inside, which a lone loop does not produce to the same degree.
• Treating an electromagnet and a permanent magnet as interchangeable — the whole point of an electromagnet is that its magnetism switches on and off with the current and its strength is adjustable, unlike a permanent magnet.
• Using the wrong core material — the core must be soft iron, not steel or any material that stays magnetised; the wrong material would leave the core permanently magnetic even with the current off.
• Reaching for $B = \mu_0 n I$ or any numerical field formula — that belongs to Class 12; at this level, describe the field pattern and its strengthening factors only in words.

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