The bar magnet as an equivalent solenoid (qualitative)
A current-carrying solenoid makes the same field pattern as a bar magnet. Each turn is a tiny magnetic dipole, and their moments add along the axis.
Why a solenoid acts like a bar magnet
A solenoid is a long coil of many turns. Each turn carrying current I is a small loop with magnetic moment IA. These moments all point the same way along the axis, so they add: the solenoid's moment is m = NIA. Inside, the fields of the turns add into a strong, nearly uniform field. Outside, the field spreads out from one end and returns to the other. So one end acts as a north pole and the other as a south pole. Hung freely, a solenoid settles north-south like a compass, and it attracts and repels other magnets. Your textbook shows that, at a far point on its axis, the solenoid's field has the same form as a bar magnet's: B = (μ₀/4π)(2m/r³). You need this idea and the result, not the derivation.
The bar magnet seen as a solenoid
Now turn the idea round. Inside a bar magnet, electrons circle round nuclei and also spin. Each acts like a tiny current loop with its own magnetic moment. In a magnet, very many of these loops are lined up. Together they behave like the turns of a solenoid. This is why a bar magnet behaves like an equivalent solenoid. The idea that all magnetism comes from circulating currents was first put forward by Ampere.
Activity: compare a solenoid with a bar magnet
You need insulated copper wire, a pencil or a cardboard tube, a cell, a key, a compass and iron filings.
- 1Wind 50 to 100 close turns of the wire on the tube to make a solenoid. Connect it to the cell through the key.
- 2Close the key. Bring the compass near each end of the solenoid. Observe: one end attracts the N pole of the needle and the other end repels it.
- 3Place the solenoid under a sheet of paper, sprinkle iron filings and tap. Observe: the pattern looks like that of a bar magnet.
- 4Reverse the current. Observe: the two ends swap their poles.
- 5Switch off the current. Observe: the solenoid stops acting as a magnet.
- 6Result: a current-carrying solenoid behaves like a bar magnet whose poles depend on the direction of the current.
Bar magnet vs solenoid
| Feature | Bar magnet | Current-carrying solenoid |
|---|---|---|
| Source of the field | Lined-up tiny current loops of electrons | Current in the turns |
| Field pattern outside | N to S, like a dipole | The same as a bar magnet |
| Magnetic moment | m, from S to N | m = NIA, along the axis |
| Can it be switched off or reversed? | No | Yes: switch off the current, or reverse it to swap the poles |
| Can its strength be changed? | No, it is fixed | Yes: change I or N, or add an iron core |
How to draw the two patterns side by side
- Left: draw a bar magnet with N and S, and its usual closed field lines.
- Right: draw a solenoid as a row of loops, or as ⊙ on top and ⊗ below. Show straight lines inside and spreading lines outside.
- Mark N at the end of the solenoid where the lines come out, and S where they go in.
- Show the current direction with arrows on the turns.
- Write under the figure: 'The patterns outside are alike.'
Worked example: magnetic moment of a solenoid
A solenoid of 500 turns has a cross-sectional area of 2.0 × 10⁻⁴ m² and carries 1.5 A. (a) Find its magnetic moment. (b) What happens to m if the current is reversed?
- (a) Formula: m = NIA.
- m = 500 × 1.5 A × 2.0 × 10⁻⁴ m² = 0.15 A m².
- (b) The size stays 0.15 A m², but m points the other way along the axis: the N and S ends swap.
(a) 0.15 A m²; (b) the same size, opposite direction
An electromagnet is a solenoid with a soft iron core. Cranes in Indian scrap yards and steel plants use giant ones to lift iron, and drop it simply by switching off the current.
2 marks: “Explain why a current-carrying solenoid behaves like a bar magnet.” Each turn is a current loop, a magnetic dipole; the moments add along the axis to m = NIA; one end acts as N and the other as S; the outside pattern and far-axis field (μ₀/4π)(2m/r³) match those of a bar magnet.
3 marks: “Draw the magnetic field lines of a bar magnet and of a current-carrying solenoid. State two similarities and one difference.” Two sketches. Similar: closed loops from N to S outside; the same far-field form. Different: the solenoid's poles reverse with the current and vanish when it is switched off.
1 marks: “Looking at one end of a solenoid, the current flows clockwise. Is that end a north or a south pole?” A south pole.
Anticlockwise = North, clockwise = South, looking at an end of the solenoid.