Bonus (Optional) Problem 5 (25pts). A Helmholtz coil (see figure below) is a structure used for creating uniform magnetic fields at the centre. Consider two thin circular coaxial coils each of radius R, having N turns, carrying a current I in the same direction and separated by a distance d. The field due to the thin wire connecting the two coils can be ignored. 00 a) Find the magnetic field B on the axis of symmetry (the x-axis) of the Helmholtz coil. b) Show that =0 at the point midway between the two coils. dr c) Show that if d = R, = 0 at the point midway between the two coils. d) Explain what your previous results in b) and c) mean.