Verify the Gauss’s law for magnetic field of a point dipole of dipole moment ${{\rm{\vec m}}}$ at the origin for the surface which is a sphere of radius $\mathrm{R}$.

Two short bar magnets of magnetic moments ' $M$ ' each are arranged at the opposite corners of a square of side ' $d$ ', such that their centres coincide with the corners and their axes are parallel to one side of the square. If the like poles are in the same direction, the magnetic induction at any of the other corners of the square is

The magnetic moment of a magnet of length $10\, cm$  and pole strength $ 4.0\, Am$  will be……$A{m^2}$

Two identical dipoles each of magnetic moment $1.0\, A-m^2$ are placed at a separation of $2\,m$ with their axes perpendicular to each other. What is the magnetic field at a point midway between the dipoles ?

A short bar magnet has a magnetic moment of $0.48\; J \;T ^{-1} .$ Give the direction and magnitude of the magnetic field produced by the magnet at a distance of $10 \,cm$ from the centre of the magnet on

$(a)$ the axis,

$(b)$ the equatorial lines (normal bisector) of the magnet.