In fig, there are two semi-circles of radii r1 and r2in which a current i is flowing. The magnetic induction at centre O will be

B= B1+B2=μ04π×πir1+μ04π×πir2=μ0i41r1+1r2=μ0i4r1+r2r1r2

In fig, there are two semi-circles of radii r1 and r2in which a current i is flowing. The magnetic induction at centre O will be

B= B1+B2=μ04π×πir1+μ04π×πir2=μ0i41r1+1r2=μ0i4r1+r2r1r2

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In fig, there are two semi-circles of radii r1 and r₂
in which a current i is flowing. The magnetic induction at centre O will be

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$\frac{μ_{0} i}{4} (r_{1} + r_{2})$

$\frac{μ_{0}^{} i}{4} (r_{1} - r_{2})$

$\frac{μ_{0} i}{4} (\frac{r_{1} + r_{2}}{r_{1} r_{2}})$

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

answer is C.

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Detailed Solution

B= B₁+B₂
$\begin{aligned} = \frac{μ_{0}}{4 π} \times \frac{πi}{r_{1}} + \frac{μ_{0}}{4 π} \times \frac{πi}{r_{2}} \\ = \frac{μ_{0} i}{4} [\frac{1}{r_{1}} + \frac{1}{r_{2}}] = \frac{μ_{0} i}{4} [\frac{r_{1} + r_{2}}{r_{1} r_{2}}] \end{aligned}$