Two short bar magnets have magnetic moments $1.2 \text{ Am}^2$ and $1.0 \text{ Am}^2$. They are placed on a horizontal table parallel to each other at a distance of $20 \text{ cm}$ between their centres, such that their north poles point towards the geographic south. They share a common magnetic equatorial line. The horizontal component of the Earth's magnetic field is $3.6 \times 10^{-5} \text{ T}$. Calculate the resultant horizontal magnetic induction at the midpoint of the line joining their centres. (Given: $\frac{\mu_0}{4 \pi} = 10^{-7} \text{ N/A}^2$)

• A
  $3.6 \times 10^{-5} \text{ T}$
• B
  $1.84 \times 10^{-4} \text{ T}$
• C
  $2.56 \times 10^{-4} \text{ T}$
• D
  $5.8 \times 10^{-5} \text{ T}$