Two long thin parallel wires and a square loop of side L are coplanar. The currents in the two wires A and B are 2 A and 1 A and total flux through the loop is zero. Nearer side of the loop is at a distance L from wire A. The separation between the wires is

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2L/3

3L/4

L/3

L/2

answer is C.

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Detailed Solution

$\int d \emptyset = \int B . dx . L \emptyset_{1} = \int \frac{μ_{o} i}{2 πx} dx . L = \frac{μ_{o} (2 i) L}{2 π} {(\log_{e}^{} x)}_{L}^{2 L}$

$\int d \emptyset = \int B . dx . L = \int \frac{μ_{o} i}{2 πx} dx . L \emptyset_{2} = \frac{μ_{o} iL}{2 π} {(\log_{e}^{} x)}_{L - d}^{2 L - d} \emptyset_{1} - \emptyset_{2} = \frac{μ_{0} (2 i) L}{2 π} \log_{e}^{} 2 - \frac{μ_{0} iL}{2 π} (\log_{e} \frac{2 L - d}{L - d}) 0 = \log_{e} 2^{2} - \log_{e} \frac{2 L - d}{L - d} 4 = \frac{2 L - d}{L - d} 4 L - 4 d = 2 L - d 2 L = 3 d d = \frac{2 L}{3}$