Magnetic Field Around Current-Carrying Wires

simulator beginner ~8 min
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B = 0.1 mT at 1 cm from a 5A wire

A wire carrying 5 amperes creates a circular magnetic field. At 1 cm distance, the field strength is about 0.1 millitesla. The field direction follows the right-hand rule: curl your right hand around the wire with thumb in the current direction, and your fingers point in the field direction.

Formula

B = μ₀I/(2πr) (Ampere's law for long wire)
F/L = μ₀I₁I₂/(2πd) (force between parallel wires)
μ₀ = 4π × 10⁻⁷ T·m/A (permeability of free space)

Magnetic Fields from Electric Currents

In 1820, Hans Christian Oersted accidentally discovered that an electric current deflects a nearby compass needle. This was the first evidence that electricity and magnetism are connected. A current-carrying wire creates a circular magnetic field around it, with the field strength proportional to the current and inversely proportional to the distance from the wire.

Ampere's Law and the Right-Hand Rule

The magnetic field around a long straight wire is given by Ampere's law: B = μ₀I/(2πr). The direction follows the right-hand rule — point your thumb along the current, and your fingers curl in the field direction. This simple relationship is the foundation of all electromagnetic technology, from electric motors to MRI machines.

Parallel Wire Interactions

Two parallel wires carrying current interact through their magnetic fields. If the currents flow in the same direction, the wires attract; if in opposite directions, they repel. This force, F/L = μ₀I₁I₂/(2πd), was historically used to define the ampere: one ampere is the current that produces a force of 2 × 10⁻⁷ N per meter between two wires one meter apart.

Applications and Technology

The magnetic field around current-carrying conductors is the operating principle behind electromagnets, solenoids, transformers, and electric motors. By coiling wire into loops, the field is concentrated and amplified. Superconducting coils carrying thousands of amperes create the powerful fields used in MRI machines (1.5-3 T) and particle accelerators (up to 16 T at the LHC).

FAQ

What is the magnetic field around a wire?

A current-carrying wire creates a circular magnetic field around it, described by Ampere's law: B = μ₀I/(2πr). The field forms concentric circles centered on the wire, with direction given by the right-hand rule.

What is the right-hand rule?

Point your right thumb in the direction of current flow. Your curled fingers show the magnetic field direction — it circles clockwise when current flows away from you, and counterclockwise when current flows toward you.

Why do parallel wires attract or repel?

Two parallel wires carrying current create magnetic fields that exert forces on each other. Same-direction currents attract (each wire sits in the other's field and experiences a force toward it). Opposite-direction currents repel.

How strong is the magnetic field from a household wire?

A typical household wire carrying 10A creates a field of about 0.04 mT at 5 cm distance — roughly 1000 times weaker than Earth's magnetic field (0.05 mT). The field drops rapidly with distance.

Sources

Embed

<iframe src="https://homo-deus.com/lab/electromagnetism/magnetic-field/embed" width="100%" height="400" frameborder="0"></iframe>
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