Inductance of a toroid formula derivation and examples

What is toroid?

The solenoid bent into circular shape is called toroid.

Inductance of a toroid derivation

Consider a toroid having rectangular cross sectional area.The inner radius of the toroid is ‘a’ while outer radius is b.The number of turns of toroid is N.Let i be the current flowing through each turn of toroid. The magnetic field lines inside the solenoid is given as:

Where dA = hdr is the area of the elementary strip of toroid .Putting the value of ‘B’ from equation (1) we get:

Which is the relation for inductance of solenoid.The inductance L depends only on geometrical factors.