Two short magnets of equal dipole moments $$M$$ are fastened perpendicularly at their centres. The magnitude of the magnetic field at a distance $$d$$ from the centre on the bisector of the right angle is ($$\mu_0=$$ Permeability of free space)

A steel wire of length $$l$$ and magnetic moment $$M$$ is bent into a semicircular arc of radius $$R$$. The new magnetic moment is

A magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing down at $$30^{\circ}$$ with the horizontal. The horizontal component of the earth's magnetic field at the place is 0.3 G . Then the magnitude of the earth's magnetic field at the location is