Torque on a magnetic dipole

The torque on dipole $m_2$ placed in the magnetic field of dipole $m_1$ is $\tau = m_2 B \sin\theta$ where $\theta$ is the angle between $\vec m_2$ and the magnetic field due to $m_1$.

Magnetic field due to a short magnetic dipole

For a dipole of magnetic moment $m_1$ at distance $r$ on its equatorial line, the magnetic field is $B = \frac{\mu_0}{4\pi}\frac{m_1}{r^3}$

Given: $m_1 = 1\,\text{A m}^2, \quad m_2 = 1\,\text{A m}^2, \quad r = OP = 1\,\text{m}$ and $\frac{\mu_0}{4\pi} = 10^{-7}$

So, $B = 10^{-7}\cdot \frac{1}{1^3} = 10^{-7}\,\text{T}$

Maximum torque

Since only the magnitudes are given, torque is taken for the perpendicular orientation: $\sin\theta = 1$

Hence, $\tau = m_2 B = 1 \times 10^{-7} = 10^{-7}\,\text{N m}$

Required integer

The torque is $\tau = 1 \times 10^{-7}\,\text{N m}$

Therefore, the required integer is 1.