Magnetism and Matter Problems - Numerical 06

The core of a toroid having 3000 turns has inner and outer radii of 11 cm and 12 cm respectively. The magnetic field in the core for a current of 0.70 A is 2.5 T. What is the relative permeability of the core?

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Suggested solution:

Suggested solution:

The magnetic field in the empty space enclosed by the windings of the toroid is given by

Where n is the number of turns per unit length and I is the current.

If the space is filled by a core of permeability m then equation (1) is rewritten as under.

Now, B=2.5 tesla, I=0.70 ampere,

mean radius=11.5cm=11.5x10^-² m

Here, we have ignored the variation of B across the cross-section of the toroid and taken the radius of the toroid to be mean of inner and outer radii.