Question

Obtain an expression for magnetic induction along the axis of toroid

Answer 1

The magnetic field induction along the axis of toroid will be B = μ₀nI

Explanation:

A toroid is a solenoid bent into the shape of a doughnut.

Let r be the radius of the toroid, B be the magnetic field produced by it, N be the number of turns, and I be the current flowing through it.

From ampere's circuital law,

∫B.dL = μ₀NI

=> B . ∫dL = μ₀NI

=> B(2πr) = μ₀NI

=> B = μ₀NI/2πr

If n is the number of turns per unit length of toroid, then

n = N/2πr

=> B = μ₀nI

which is the required expression for magnetic field induced along the axis of toroid.