First slide

Toroid

Question

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

Moderate

A

484
B

584
C

384
D

684

Solution

$\begin{array}{rcl} B & = & \frac{μNi}{2 πr}; r = \frac{11 + 12}{2} x 10^{- 2}; \\ μ & = & \frac{2 πrB}{Ni} \\ μ_{r} & = & \frac{μ}{μ_{0}} = \frac{2 π x 11.5 x 10^{- 2} x 2.5}{4 π x 10^{- 7} x 3 x 10^{3} x 0.7} = 684 \end{array}$

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