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Two current carrying wire of infinite length are placed perpendicular to x – y plane at x = 0 and $x = R \sqrt{3}$ as shown in figure. Current in both the wires is same and inwards to the x-y plane. Find ratio of $| \int \vec{B} . \vec{d l} |$ in segment CDA to segment ABC (Consider the radius of the circle ABCD to be R).

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Detailed Solution

$\frac{\int \vec{B} . \vec{d l} C D A}{\int \vec{B} . \vec{d l} A B C} = \frac{\frac{μ_{0} I}{2} + \frac{μ_{0} I}{2 π} \frac{π}{6} \times 2}{\frac{μ_{0} I}{2} - \frac{μ_{0} I}{2 π} (\frac{π}{6}) \times 2}$

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