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Q.

An infinitely long straight conductor is bent into the shape as shown in the figure. It carries a current of $i$ ampere and the radius of the circular loop is $r$ metre. Then the magnetic induction at its centre will be

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a

$\frac{μ_{0}}{π} \frac{2 i}{r} (π + 1)$

b

$\frac{μ_{0}}{4 π} \frac{2 i}{r} (π - 1)$

c

zero

d

infinite

answer is B.

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Detailed Solution

$B = \frac{μ_{0} i}{2 r} - \frac{μ_{0}}{2 π} \cdot \frac{i}{r}$

$= \frac{μ_{0}}{4 π} \times \frac{2 i}{r} [π - 1]$

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An infinitely long straight conductor is bent into the shape as shown in the figure. It carries a current of i ampere and the radius of the circular loop is r metre. Then the magnetic induction at its centre will be