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Question

# The core of a toroid having 3000 turns has inner and outer radial 11 cm and 12 cm respectively. The magnetic field in the core for a current of 0.7 A is 2.5 T. Calculate the relative permeability of the core ?

A
684
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B
290
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C
395
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D
768
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Solution

## The correct option is A 684Given: N=3000; r1=11 cm; r2=12 cm i=0.7 A and B=2.5 T So the mean radius of toroid will be r=r1+r22=11.5 cm=11.5×10−2 m Magnetic field produced by toroid inside the core of toroid is given by B=μ0μrNi2πr 2.5=4π×10−7×μr×3000×0.72π×11.5×10−2 μr=2.5×2π×11.5×10−24π×10−7×3000×0.7 ∴μr≈684 Hence, option (a) is correct. Why this question ? Concept : Magnetic field, B=μni Here, μ=μ0μr

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