A galvanometer coil has $500$ turns and each turn has an average area $3\times 10^{-4}m^{2}$. If a torque of $1.5\; Nm$ is required to keep this coil parallel to a magnetic field when a current of $0.5 \; A$ is flowing through it, the strength of the field (in $T$) is _______. Option: 1 20 Option: 2 10 Option: 3 22 Option: 4 30

As coil is parallel to magnetic field, the Area vector or Magnetic Moment is perpendicular to magnetic field i.e., $\theta= 90^{0}$

Torque applied due to magnetic field when angle between magnetic moment and magnetic field $\theta$ is

$\tau = MB\sin \theta= NIAB\sin \theta$

$\\N=500 turns \\A=3\times 10^{-4}m^{2} \\\tau_{external} = 1.5Nm \\I=0.5A$

$\\\tau =1.5= 500\times 0.5\times 3\times 10^{-4}B\sin \90^{0} \\B=20 T$

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