4.4 Magnetic Fields Created by Current-Carrying Wires

Current creates a magnetic field

Any current-carrying wire produces a magnetic field that circles around it. Use the right-hand rule: point your thumb in the direction of conventional current, and your curled fingers show the direction of the field loops around the wire. The field lines form concentric circles centered on the wire.

Field strength around a straight wire

The magnetic field magnitude from a long straight wire is B = μ₀I / (2πr), where I is current, r is distance from the wire, and μ₀ is the permeability of free space (4π×10⁻⁷ T·m/A). Field strength increases with current and decreases with distance from the wire.

Loops and solenoids

A current loop acts like a magnetic dipole, with field lines emerging from one face (like a north pole) and entering the other. Stacking loops into a solenoid creates a strong, uniform field inside, similar to a bar magnet, useful for generating controlled magnetic fields.

Key terms

Right-hand rule (wire)

Point thumb in direction of current; curled fingers show the circular direction of the magnetic field around the wire.

B = μ₀I/(2πr)

Magnetic field magnitude at distance r from a long straight current-carrying wire.

μ₀ (permeability of free space)

Constant equal to 4π×10⁻⁷ T·m/A relating current and distance to magnetic field strength.

Current loop field

Acts like a magnetic dipole: field lines exit one face (north-like) and enter the other (south-like).

Solenoid

A coil of current loops producing a strong, uniform magnetic field inside, similar to a bar magnet.

Try an AP-style question

The distance from a long straight current-carrying wire doubles. What happens to the magnetic field?

1. It halves
2. It doubles
3. It stays the same
4. It becomes ¼