At the beginning of the nineteenth century, the magnetic field of wires carrying currents was the focus of investigations in physics, both experimentally and theoretically. A particularly interesting case is that of a very long wire, carrying a constant current I, which has been bent into the form of a ‘V’, with opening angle 2θ. According to Ampere’s computations, the magnitude ` B of the magnetic field at a point P lying outside the ‘V’, but on its axis of symmetry and at a distance d from its vertex, is proportional to tan(θ/2). However, for the same situation, Biot and Savart suggested that the magnetic field at P might be proportional to θ. In fact, they attempted to decide between the two possibilities by measuring the oscillation period of a magnetic needle as a function of the ‘V’ opening angle. However, for a range of θ values, the predicted differences were too small to be measured. (i) Which formula might be correct? (ii) Find the proportionality factor in this formula and guess the most likely factor appearing in the other one.