Electricity & Megnetism

# Inductance of a toroid formula derivation and examples

**What is toroid?**

The solenoid bent into a circular shape is called a toroid.

## Inductance of a toroid derivation

Consider a toroid having a rectangular cross-sectional area. The inner radius of the toroid is â€˜aâ€™ while the outer radius is b. The number of turns of the toroid is N. Let I will be the current flowing through each turn of the toroid. The magnetic field lines inside the solenoid are given as:

Where dA = hdr is the area of the elementary strip of the toroid. Putting the value of â€˜Bâ€™ from equation (1) we get:

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

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