It is theoretically possible to create a triangular Helmholtz pair. Wolfgang Wiltschko (pictured) at Frankfurt University for studying magnetic navigation in birds Large octagonal Helmholtz coil used by Prof.
28) They can be used for generating magnetic field with specific non-uniformity, such as in the Penning trap. There are many other configuration with multiple coils which are provided commercially, both with different dimensions of sub-coils as well as those resembling solenoidal arrangement (with the same radius for all sub-coils). On the other hand, spherical coils can be used as sensors, because they detect magnetic field which is proportional to the field at the geometrical centre of such coil. 26) However, such a shape there is no access to the inside of the coil and thus the practical applicability is highly limited. With an appropriate arrangement of turns and current intensity it is possible to achieve very uniform field in a spherical coil. 24)įor an ordinary Helmholtz pair the optimal angle is 63.4°. Additionally, the turn ratio should be N 1 /N 2 = 0.68212, the radius ratio r 1 /r 2 = 0.67189, and the distance ratio q 1 /q 2 = 2.685. The positioning is such that the first pair is located at the intersection of 40.09° and the second pair at 73.43° angle with the outline of the sphere, as illustrated. With four coils, also known as a double Helmholtz coil or double-pair Helmholtz coil, they can be also distributed over a sphere, further increasing the uniformity. Such name of Maxwell coil (denoting the gradient coil) is used especially in the particle accelerators, 20) and magnetic resonance imaging. r (see detailed description in the following sections).The name gradient Maxwell coil is also used when referring to an anti-Helmholtz pair separated by the distance of √3 The current can be equal in each coil, but the ratio of ampere-turns must be matched so that outer/inner = 49/64 (if the current is the same then the turns must have such ratio of 49/64). (1) Magnetic field at the centre of a Helmholtz coil
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