Question

17.1) Helmholtz coils

The magnetic field on the axis of a circular loop of wire is not very uniform (in fact, we showed that the field

strength decreases as 1/r3

). But, with two such coils, one can produce a relatively uniform field in a small

neighborhood.

Consider two parallel circular coils of radius a, centered on the y-axis. One coil is in the y = 0 plane, and the

other is in the y = d plane. Assume that the current I in each coil flows in the same direction.

(a) Compute the magnetic field at a point y0, between the loops, on the y-axis.

(b) At the midpoint between the two coils (i.e., at y0 =

1

2

d), show that the first derivative of the magnetic field

vanishes

dB

dy

y= d

2

= 0. (1)

This means that the field varies very little in the y direction at this point.

Answer 1