The magnetic field at the centre of a wire loop formed by two semicircular wires of radii R1=2π m and R2=4π m carrying current I = 4A as per figure given below is α×10−7T.The value of α is (Centre O is common for all segments)

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The magnetic field at the centre of a wire loop formed by two semicircular wires of radii $R_{1} = 2 π m$ and $R_{2} = 4 π m$ carrying current I = 4A as per figure given below is $α \times 10^{- 7} T .$ The value of $α$ is (Centre O is common for all segments)
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$3 π$

$2 π$

answer is B.

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Detailed Solution

$\frac{μ_{0} i}{2 R_{2}} (\frac{π}{2 π}) \otimes + \frac{μ_{0} i}{2 R_{1}} (\frac{π}{2 π}) \otimes$
$(\frac{μ_{0} i}{4 R_{2}} + \frac{μ_{0} i}{4 R_{1}}) \otimes$
$\begin{array}{l} \frac{4 π \times 10^{- 7} \times 4}{4 \times 4 π} + \frac{4 π \times 10^{- 7} \times 4}{4 \times 2 π} \\ = 3 \times 10^{- 7} = α \times 10^{- 7} \\ α = 3 \end{array}$