Cylindrical shields formed from material of high permeability are commonly used in providing low-magnetic field environments for experimental research. Cylindrical coils are often sited inside such shields to produce controlled patterns of field variation, but interaction of the coils with the mu-metal distorts the fields. Here we show how to analytically calculate the fields that are produced by simple coils inside a finite-length, cylindrical mu-metal shield with end-caps, and report experimental measurements on two different coils (loop and saddle), demonstrating excellent agreement with the theory. Optimal spacings of Helmholtz-type coils inside finite-length shields are also derived using the analytic expressions.
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