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  4. Two current carrying wire of infinite length are placed perpendicular to x-y plane at x= 0 and x=R √3 as shown in figure. Current in both the wires is same and inwards to the x-y plane. Find ratio of ∫ vecB ⋅ vecd l in segment C D A to segment A B C will be: <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-tclhyliq1khaf6dm.jpg />

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Q. 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 $\int \vec{B} \cdot \vec{d} l$ in segment $C D A$ to segment $A B C$ will be:
Question

NTA AbhyasNTA Abhyas 2022

Solution:

$\frac{\int \vec{B} \cdot \vec{d l} CDA }{\int \vec{B} \cdot \vec{d l} ABC }=\frac{\frac{\mu_{0} I}{2}+\frac{\mu_{0} I}{2 \pi} \frac{\pi}{6} \times 2}{\frac{\mu_{0} I}{2}-\frac{\mu_{0} I}{2 \pi} \frac{\pi}{6} \times 2}=2$