A long straight wire carrying a current $$i=10\,\text{A}$$ and a rectangular metallic loop of dimensions $$b\times c$$ lie in the same plane as shown in the figure. The parameters are $$a=10\,\text{cm}$$, $$b=30\,\text{cm}$$ and $$c=50\,\text{cm}$$. The mutual inductance of the system is nearly

A

$$69\,\text{nH}$$

B

$$71\,\text{nH}$$

C

$$139\,\text{nH}$$

D

$$281\,\text{nH}$$