State the qualitative variation of the strength of the magnetic field around straight wires and solenoids

4.5.3 Magnetic Effect of a Current

Learning objective

State the qualitative variation of the magnetic‑field strength around straight wires and long solenoids, describe how the field direction is obtained, outline simple experiments that reveal the field pattern, and give examples of everyday devices (relay, loud‑speaker) that rely on the magnetic effect of a current.

Key concepts

• A current‑carrying conductor always produces a magnetic field that forms closed loops around the conductor.
• The magnetic field B is a vector quantity – it has magnitude (strength) and direction.
• For a long straight wire the field lines are concentric circles centred on the wire; inside a long solenoid the field is almost uniform and parallel to the axis.
• All relationships required by the Cambridge IGCSE/A‑Level syllabus are qualitative – numerical constants such as μ₀ are not needed.

Right‑hand rule (direction of the field)

Grip the conductor with the right hand so that the thumb points in the direction of conventional current (positive to negative). The curled fingers then give the direction of the magnetic‑field lines.

• Reversing the current reverses the sense of the field.

Magnetic field around a straight wire

Pattern and direction

• The field forms concentric circles centred on the wire.
• At any point the field direction is tangent to the circle and follows the right‑hand rule.
• Reversing the current reverses the sense of the circular field.

Qualitative variation of the field strength

• Current (I): stronger current → stronger field B ∝ I
• Distance from the wire (r): the farther away, the weaker the field B ∝ 1/r
• Direction of current: reversing the current reverses the direction of the circular field (right‑hand rule).

Simple visual‑isation experiment

1. Lay a straight piece of insulated copper wire on a sheet of paper.
2. Place a small compass at several positions around the wire and note the needle direction, or sprinkle fine iron filings over the wire and tap gently.
3. The compass needles (or filings) arrange themselves in concentric circles, confirming the circular pattern and the right‑hand‑rule direction.

Magnetic field inside a long solenoid

Pattern and direction

• Inside the solenoid the field lines are parallel to the axis and nearly uniform.
• Outside the coil the lines diverge and the field becomes weak.
• Using the right‑hand rule with the fingers curled in the sense of the winding, the thumb points from the South‑pole end toward the North‑pole end – this is the direction of the field inside the solenoid.

Qualitative variation of the field strength

• Current (I): higher current → stronger field B ∝ I
• Turn density (n): more turns per unit length → stronger field B ∝ n
• Core material: inserting a ferromagnetic core multiplies the field by its relative permeability μᵣ (soft iron ≈ 500–2000).
• Length of the solenoid (for a fixed total number of turns): a longer coil reduces turn density n and therefore reduces B.
• Coil radius: for a given n and I, a larger radius spreads the field over a larger area, making the field at the centre slightly weaker.

Simple visual‑isation experiment

1. Wind a long coil of insulated wire tightly around a cylindrical former (e.g., a cardboard tube).
2. Place a small compass at the centre of the coil and another a short distance outside the coil.
3. The inner compass aligns with the axis of the coil (uniform field); the outer compass shows a weak, non‑uniform field that fans outward.

Real‑world applications (magnetic effect of a current)

• Relay: A solenoid coil creates a magnetic field when current flows. The field pulls a ferromagnetic armature, opening or closing a separate set of contacts. When the current stops, a spring returns the armature.
• Loud‑speaker: A coil attached to a diaphragm sits in the gap between the poles of a permanent magnet. An alternating current through the coil produces a changing magnetic field that makes the coil (and thus the diaphragm) vibrate, producing sound.

Safety and practical limits

• High currents cause heating (I²R losses); wires must be sized to avoid excessive temperature rise.
• Never touch a live coil while current is flowing – the magnetic field can attract ferromagnetic objects with enough force to cause injury.
• When using a ferromagnetic core, ensure it is not saturated; otherwise the field will no longer increase proportionally with current.

Summary of qualitative variation

Quick revision – key statements

• For a straight conductor, the magnetic field forms concentric circles; its strength increases with current and decreases with distance from the wire.
• Inside a long solenoid the field is approximately uniform and parallel to the axis; its strength increases with current, turn density and core permeability, and decreases with coil length or radius.
• The direction of the field is given by the right‑hand rule; reversing the current reverses the field direction.
• Simple experiments with a compass (or iron filings) clearly demonstrate the field patterns for both a straight wire and a solenoid.
• Relays and loud‑speakers are classic devices that exploit the magnetic effect of a current.