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A very long straight wire is bent as shown into a nearly circular part of radius r metre. A constant current ‘i’ ampere is passed through it. The magnetic flux density at thecentre of the circle (in tesla) is

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$(\frac{2 i}{r}) \times 10^{- 7}$

$\frac{2 i (π - 1)}{r} \times 10^{- 7}$

$(\frac{2 π i}{r}) \times 10^{- 7}$

$\frac{2 i (π + 1)}{r} \times 10^{- 7}$

answer is D.

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Detailed Solution

$B = B_{s t} + B_{circle} \begin{array}{l} B_{s t} = \frac{μ_{o} i}{2 π R} (outwards) \\ B_{C} = \frac{μ_{o} i}{2 R} (inwards) \\ B = \frac{μ_{o} i}{2 R} (1 - \frac{1}{π}) \end{array}$

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