A wire is bent in the form of a semicircle of radius $r$ and carries a current of $i$ . The magnetic induction at the centre of the semicircle is

\frac{μ_{o} i}{2 r}

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\frac{μ_{o} i}{8 r}

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\frac{μ_{o} i}{4 r}

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\frac{μ_{o} i}{r}

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Solution

The correct option is C $\frac{μ_{o} i}{4 r}$
B for semicircle $= \frac{μ_{0} i}{4 π r} (θ)$
$= \frac{μ_{0} i}{4 π r} (π)$
$= \frac{μ_{0} i}{4 r}$

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A wire is bent in the form of a semicircle of radius $r$ and carries a current of $i$ . The magnetic induction at the centre of the semicircle is

The correct option is C $\frac{μ_{o} i}{4 r}$
B for semicircle $= \frac{μ_{0} i}{4 π r} (θ)$
$= \frac{μ_{0} i}{4 π r} (π)$
$= \frac{μ_{0} i}{4 r}$