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:

Question

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" /> (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

(∫ vecB ⋅ vecd l CDA /∫ vecB ⋅ vecd l ABC )=((μ0 I/2)+(μ0 I/2 π) (π/6) × 2/(μ0 I)2-(μ0 I)2 π (π/6) × 2=2

Q. 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 $\int B \cdot d l$ in segment $C D A$ to segment $A BC$ will be:

$\frac{\int B \cdot d l C D A}{\int B \cdot d l A BC} = \frac{\frac{μ _{0} I}{2} + \frac{μ _{0} I}{2 π} \frac{π}{6} \times 2}{\frac{μ _{0} I}{2} - \frac{μ _{0} I}{2 π} \frac{π}{6} \times 2} = 2$

Q. Two current carrying wire of infinite length are placed perpendicular to x−y plane at x= 0 and x=R3​ as shown in figure. Current in both the wires is same and inwards to the x−y plane. Find ratio of ∫B⋅dl in segment CDA to segment ABC will be:

∫B⋅dlABC∫B⋅dlCDA​=2μ0​I​−2πμ0​I​6π​×22μ0​I​+2πμ0​I​6π​×2​=2

Q. 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 $\int B \cdot d l$ in segment $C D A$ to segment $A BC$ will be:

$\frac{\int B \cdot d l C D A}{\int B \cdot d l A BC} = \frac{\frac{μ _{0} I}{2} + \frac{μ _{0} I}{2 π} \frac{π}{6} \times 2}{\frac{μ _{0} I}{2} - \frac{μ _{0} I}{2 π} \frac{π}{6} \times 2} = 2$