Along straight wire carries a current $I$. A rectangular loop of sides $a$ and $b$ is placed in the same plane such that the side of length $a$ is parallel to the wire at a distance $d$ from it. What is the mutual inductance between the wire and the loop?

1. A.$\frac{{\mu }_{0}a}{2\pi }\ln \left(\frac{d+b}{d}\right)$
2. B.$\frac{{\mu }_{0}b}{2\pi }\ln \left(\frac{d+a}{d}\right)$
3. C.$\frac{{\mu }_{0}ab}{2\pi d}$
4. D.$\frac{{\mu }_{0}a}{2\pi }\ln \left(\frac{d}{d+b}\right)$