A pair of identical coils, each having a radius of 50cm, are separated by a distance equal to their radii, that is ,50cm. Called Helmholtz coils, they are coaxial and carry equal currents in directions such that their axial fields are in the same direction. a feature of helmholtz coils is that the resultant magnetic field in the region between the coils is very uniform. assume the current in each is 15A and there are 300 turns for each coil.

a) Align the coils so that the axis is along the z-axis, such that one coil is at -R/2 and the other is at R/2. Draw a picture of the arrangement and label the positions. indicate the direction of the current in each coil, so that the B-field is in the positive z-direction.

b) Write an equation for the B-field along the z-axis for one of the coils.

c) Write in equation for the B-field along the z-axis for both coils combined. simplify as much as you can, but there will remain two terms.

d) Over what range of z does the field vary by less than 20%.