Toroid

Advanced

Field within a doughnut-shaped coil.

Key relationB = μ₀NI/2πr

A doughnut-shaped coil confines the field entirely inside: B = μ₀NI/(2πr), depending on radius.

Worked example

N = 500, I = 2 A, r = 10 cm: 2 mT.

Common mistake

No field outside the toroid.

In more detail

A toroid is a solenoid bent into a ring. Its field is confined inside the ring and is B = μ0NI/(2πr), so there is almost no external field.

Toroidal transformers and inductors have low electromagnetic leakage.
Tokamak fusion reactors use toroidal fields to confine plasma.
Transformers and some sensors use toroidal coils, where the field stays inside the doughnut and the leakage is small.

Why is the field outside zero?

Because the field lines are closed loops inside the toroid, so nothing escapes outside.

What is a major advantage?

Little stray field, which reduces interference with nearby electronics.

Why is a toroid better than a solenoid?

Its field is confined inside the ring, so there is little stray field outside, which reduces interference.