Two circular coils $P$ and $Q$of $100$ turns each have same radius of $\pi \mathrm{cm}$. The currents in $\mathrm{P}$ and $\mathrm{R}$ are $1 \mathrm{~A}$ and $2 \mathrm{~A}$ respectively. $\mathrm{P}$ and $\mathrm{Q}$ are placed with their planes mutually perpendicular with their centers coincide. The resultant magnetic field induction at the center of the coils is $\sqrt{\mathrm{x}} \mathrm{mT}$, where X=___.

$\left[\text { Use } \mu_0=4 \pi \times 10^{-7} \mathrm{TmA}^{-1}\right]$

  • [JEE MAIN 2024]
  • A

    $10$

  • B

    $20$

  • C

    $30$

  • D

    $40$

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  • [AIIMS 2019]