Two short bar magnets have their magnetic moments $1.2\;Am^2$ and $1.0\;Am^2$. They are placed on a horizontal table parallel to each other at a distance of $20\;cm$ between their centers, such that their north poles pointing towards geographic south. They have common magnetic equatorial line. Horizontal component of earth's field is $3.6 \times 10^{-5}$ T. Then, the resultant horizontal magnetic induction at mid point of the line joining their centers is $\bigg(\large\frac{\mu _0}{4 \pi}$$=10 ^{-7} 11/m\bigg)$

Question

$$(a)\;3.6 \times 10^{-5}T \quad (b)\;1.84 \times 10^{-4}\;T \quad (c)\;2.56 \times 10^{-4}\;T \quad (d)\;5.8 \times 10^{-5}T$$