Question

give the magnetic induction around the axis of toroid.... ​

Answer 1

If a solenoid is bent in a circular shape and the ends are joined, we get a toroid. Alternatively, one can start with a nonconducting ring and wind a conducting wire closely on it. The magnetic field in such a toroid can be obtained using Ampere's Law.

MAGNETIC FIELD DUE TO A TOROID - EXAMPLE

concept

The magnetic field in the open space inside (point P) and exterior to the toroid (point Q) is zero. The field B inside the toroid is constant in magnitude for the ideal toroid of closely wound turns.The direction of the magnetic field inside is clockwise as per the right-hand thumb rule for circular loops. Three circular Amperian loops 1, 2 and 3 are shown by dashed lines. By symmetry, the magnetic field should be tangential to each of them and constant in magnitude for a given loop.

Example:The number of turns per unit length in a toroid is 10

3

and current flowing in it is

4π

1

ampere, then the magnetic induction produced in it, is :

Magnetic field in a toroid B=μ

0

Given n=10

3

and i=

4π

1

A

We know that μ

0

=4π×10

−7

T/A

B=4π×10

−7

×10

3

×

4π

1

=10

−4

T