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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