First slide

Magnetic field due to current element

Question

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 …….

Moderate

Solution

$A v e r a g e r a d i u s = r = \frac{r_{i} + r_{o}}{2} = \frac{11 + 12}{2} = 11.5 c m I n s i d e T o r o i d, B = \frac{μ N i}{2 π r} \Rightarrow μ = \frac{2 π r B}{N i} W e k n o w, μ_{r} = \frac{μ}{μ_{o}} \Rightarrow μ_{r} = \frac{2 π r B}{μ_{o} N i} = \frac{2 \times π \times 0.115 \times 2.5}{4 π \times 10^{- 7} \times 3000 \times 0.7} = 684.52$

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