Magnetic field due to a current

Oersted's experiment. A compass needle placed near a straight wire deflects the moment current flows, and reverses its deflection when the current is reversed. Because a compass needle only responds to magnetic fields, this proves that the current itself is the source of a magnetic field — nothing needs to be magnetised for magnetism to appear, moving charge is enough.

The straight wire. The field lines around a long straight current-carrying wire form concentric circles lying in planes perpendicular to the wire, centred on the wire itself. There is no beginning or end to any line — each closes on itself around the wire. The circles are closely spaced near the wire (a strong field) and spread out with increasing distance (a weakening field).

Direction — the right-hand thumb rule. Grasp the wire with the right hand so the extended thumb points along the direction of conventional current. The fingers, curling naturally around the wire, point in the direction the field circles. Reverse the current and every field line reverses with it — this is the same reversal Oersted saw as a flipped compass deflection.

The circular loop. Bend the straight wire into a loop and every small segment still produces its own circular field, by the same rule applied locally at each point. Inside the loop, these local fields all point the same way and add up, producing one strong, concentrated field straight through the centre — a pattern that looks like the field near a bar magnet's pole. Outside the loop the lines curve back around, exactly as they did for the straight wire.

The solenoid. A solenoid is a long coil of insulated wire with many closely spaced turns. Every turn contributes a loop-field, and because all the turns carry current in the same direction, their central fields reinforce along the whole length of the coil. The result: a field that is strong and nearly uniform inside the solenoid, running parallel to its axis, and that emerges from one end and curves around to re-enter the other outside — indistinguishable in pattern from a bar magnet's field. One end behaves as a north pole, the other as a south pole; which end is which follows from the thumb rule applied to the direction of winding and current.

The electromagnet. Wrap the same many-turn coil around a core of soft iron and pass current through it: the core is strongly and easily magnetised while current flows, but loses almost all of that magnetism the instant the current stops. This is what makes it an electromagnet rather than a permanent magnet — it can be switched on and off. Its strength can be increased in three independent ways: more turns in the coil, a larger current, and a soft iron core in place of air (soft iron responds to and amplifies the field far more than air does). Electromagnets do real work in the electric bell, the relay, and industrial cranes that lift and drop scrap iron on demand.

(This is a descriptive, field-pattern topic — ICSE excludes the numeric formulas $B = \mu_0 I / 2\pi r$ and $B = \mu_0 n I$, so there is no algebraic derivation. What follows is the reasoning chain showing why the loop and solenoid patterns arise from the single straight-wire rule — worth reconstructing on demand, not memorising as three separate facts.)

Step 1 — start from one rule. Everything above rests on exactly one fact: a straight current-carrying wire is surrounded by circular field lines whose direction is fixed by the right-hand thumb rule. Every other shape in this topic is this one rule, applied piece by piece and added up.

Step 2 — treat a loop as many tiny straight pieces. A circular loop is, at small enough scale, made of tiny nearly-straight segments, each producing its own small circular field by the thumb rule. At the loop's centre, every one of these contributions points the same direction (perpendicular to the loop's plane), since current everywhere on the loop circulates the same way. Fields pointing the same way add rather than cancel, so the many small contributions combine into one strong field straight through the centre.

Step 3 — stack many loops to get a solenoid. A solenoid is many circular loops placed side by side, all carrying current in the same sense. Each loop reinforces its central field as Step 2 showed, and because the loops are close together, their "through-the-centre" fields overlap and merge inside the coil into one long, nearly uniform field along the axis. Outside the coil, the lines curve around from one end to the other, exactly like a bar magnet's external field — a solenoid resembles a bar magnet for the same reason many stacked loop-fields reinforce.

Step 4 — add a core to amplify, not create. The soft iron core does not produce a field from nothing — it responds to the solenoid's field by becoming magnetised itself, and that magnetised core adds its own much larger field to the coil's, boosting total strength while current flows. Since soft iron does not retain this induced magnetism well, the amplification vanishes once the current stops.

A straight vertical wire carries current flowing upward. A small compass is placed to the east of the wire, in the same horizontal plane. Which way does the compass needle's north pole point, and what happens if the current is reversed?

Step 1 — apply the right-hand thumb rule. Point the right thumb upward, along the current. The curled fingers show the field circling counter-clockwise when viewed from above (looking down at the wire from the top).

Step 2 — find the field direction at the compass's location. The compass sits due east of the wire. Tracing the counter-clockwise circle (as seen from above) through the point east of the wire, the field there points toward geographic north.

Step 3 — read off the compass deflection. A compass needle's north pole aligns with the local field. The needle's north pole points north at that location — this is precisely Oersted's original observation.

Step 4 — reverse the current. Reversing the current reverses the thumb direction, so the field now circles clockwise (as seen from above); at the same eastern point the field now points south, and the compass needle's north pole swings to point south instead. The deflection exactly reverses, confirming that field direction is tied to current direction.

• Trying to use the numerical formulas $B = \mu_0 I/2\pi r$ or $B = \mu_0 n I$ on an ICSE paper — these are explicitly outside the syllabus; only the qualitative shape and direction of the field are examinable here.
• Mixing up the right-hand thumb rule (field due to a current) with Fleming's Left-Hand Rule (force on a current-carrying conductor in a field) or Fleming's Right-Hand Rule (induced EMF) — three different rules for three different situations.
• Assuming an electromagnet stays magnetised after the current is switched off — with a soft iron core it loses almost all its magnetism, unlike a permanent steel magnet.
• Forgetting that reversing the current reverses the field direction, and hence flips which end of a loop, solenoid, or electromagnet acts as the north pole.

Ask the tutor: Want to work through more right-hand thumb rule direction problems, or see how the loop-to-solenoid field-adding argument extends to why more turns means a stronger electromagnet?