A triangular loop ABCA of resistance ‘R’ is placed at a distance ‘a’ from a long straight current carrying wire having current I. Choose the correct options.

If the coil is rotated by ${180}^{\text{o}}$ about side AB, the charge flow in the loop is $\frac{{\mu }_{0}ia}{\pi R}\ell n\left(\frac{{\displaystyle 4}}{{\displaystyle 3}}\right)$

Mutual inductance of the system in the given position is $\frac{{\mu }_{0}a}{2\pi }[1-\ell n2].$

If the coil is rotated by ${180}^{\text{o}}$ about side AB, the charge flow in the loop is $\frac{{\mu }_{0}ia}{2\pi R}\ell n\left(\frac{{\displaystyle 27}}{{\displaystyle 16}}\right)$

Mutual inductance of the system in the given position is $\frac{{\mu }_{0}a}{2\pi }[1+\ell n2]$