Magnetic Properties of Ma question bank (Physics)

Two identical small bar magnets each of dipole moment $3\sqrt{5}$ J/T are placed at a center to center separation of $10$ cm, with their axes perpendicular to each other as shown in figure. The value of magnetic field at the point P midway between the magnets is $\alpha \times 10^{-3}$ T. The value of $\alpha$ is ______.
($\mu_0=4\pi \times 10^{-7}$ Tm/A)

A bar magnet has total length $2 l=20$ units and the field point $P$ is at a distance $\mathrm{d}=10$ units from the centre of the magnet. If the relative uncertainty of length measurement is $1 \%$, then uncertainty of the magnetic field at point P is :