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

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a

484

b

584

c

384

d

684

answer is D.

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Detailed Solution

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$\begin{aligned} B = \frac{μNi}{2 πr} \Rightarrow μ = \frac{2 πrB}{Ni}; r = \frac{11 + 12}{2} \times 10^{- 2}; \\ μ_{r} = \frac{μ}{μ_{0}} = \frac{2 π \times 11 .5 \times 10^{- 2} \times 2 .5}{4 π \times 10^{- 7} \times 3 \times 10^{3} \times 0 .7} = 684.5 \end{aligned}$

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