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Magnetic field effects (MFE) of radical pair (RP) recombination in micelles are investigated both analytically and numerically. The confinement effect of a micelle is modeled by a spherically symmetric potential well. The results show that the contribution from ST - transitions to all kind of MFEs is significantly increased due to the confinement effect. The spin exchange relaxation is also increased causing the ST 0 -contribution to CIDEP to be essentially reduced. Surprisingly a pronounced effect of ST + transitions on CIDEP is found when the confinement is strong. Simple analytical expressions for the recombination probability and for CIDNP and CIDEP are rigorously derived and a high accuracy is found by comparison with the numerical results. The results are interpreted in terms of a simple supercage model which is based on the assumption that the process can be separated into two stages: (1) a fast initial geminate stage in which the radicals are thermalised within the micelle and (2) a slower decay of a quasi-equilibrium state by escape from the micelle.