Magnetic Fields from Currents

A moving electric charge creates a magnetic field around it, so any current-carrying wire is surrounded by circular magnetic field lines. If you bend that wire into a coil, the field lines from each loop add up inside to make one strong, uniform field running down the coil's length. Pack in more turns of wire, or push more current through it, and the field inside gets stronger.

B = μ₀ · N · I / L

• B — magnetic field (T): the strength of the magnetic field inside the coil
• μ₀ — permeability of free space (T·m/A): a fixed constant that sets how strongly a current produces a magnetic field
• N — number of turns (turns): how many loops of wire make up the coil
• I — current (A): how much charge flows through the wire each second
• L — length (m): the length of the coil that the turns are wound over

A coil (solenoid) has 500 turns of wire wound over a length of 0.5 meters, carrying a current of 2 amps. What is the magnetic field strength inside?

• N = 500 turns
• I = 2 A
• L = 0.5 m

1. B = μ₀ · N · I / L
2. B = (4π × 10⁻⁷ T·m/A) · 500 · 2 A / 0.5 m

B = 8π × 10⁻⁴ T

The solenoid now has 1000 turns instead of 500, with the same current and length. What happens to the magnetic field inside?

• It doubles to 16π × 10⁻⁴ T
• It's cut in half to 4π × 10⁻⁴ T
• It stays the same at 8π × 10⁻⁴ T

Around a single straight wire carrying current, with no coil involved, what shape do the magnetic field lines make?

• A uniform field like inside a coil
• Straight lines running along the wire
• Circles wrapped around the wire