question_answer 15)

For a circular coil of radius R and N turns carrying I, the magnitude of the magnetic field at a point on its axis at a distance from its centre is given by,                 (a) Show that this reduces to the familiar result for field at the centre of the coil.                 (b) Consider two parallel co-axial circular coils of equal radius R, and number of turns N, carrying equal currents in the same direction, and separated by a distance R. Show that the field on the axis around the mid-point between the coils is uniform over a distance that is small as compared to R, and is given by,                 approximately.                 (Such an arrangement to produce a nearly uniform magnetic field over a small region is known as Helmholtz coils.)  

Answer:

                (a) Refer article 4.2.2. of ?Dinesh New Millennium Physics XII?                 (b) Let there be two coils as mentioned in the statement. Magnetic field in a small region of length 2d about the mid-point of the space between the two coils is given by,                                                                                 terms containing and higher powers of  are neglected.