Modeling skin effect in large magnetized iron detectors

The experimental problem of the calibration of magnetic field in large iron detectors is discussed. Emphasis is laid on techniques based on ballistic measurements as the ones employed by MINOS or OPERA. In particular, we provide analytical formulas to model the behavior of the apparatus in the transient regime, keeping into account eddy current effects and the finite penetration velocity of the driving fields. These formulas ease substantially the design of the calibration apparatus. Results are compared with experimental data coming from a prototype of the OPERA spectrometer.