Final answer:
Calculating the anomalous magnetic moment of a muon involves complex quantum mechanics, but the classical magnetic moment is found using the formula μ = IA. For calculations involving orbits, Bohr model equations modified for muon's mass are used. Experimentally, these moments are measured and compared to theoretical models for precision.
Step-by-step explanation:
To calculate the anomalous magnetic moment of the muon, sophisticated quantum physics calculations involving Quantum Electrodynamics (QED) are required. However, for a simple estimation, understanding the classical concept of the magnetic moment is necessary. The classical magnetic moment μ can be calculated by the current times the area of the loop, μ = IA = (2.0 × 10-3 A)(π(0.02 m)2) = 2.5 × 10-6 A⋅m2.
An anomalous magnetic moment arises due to quantum corrections to this classical value. The calculation itself involves comparing the experimental value and the theoretical value determined through intricate mathematics, which often involves the use of Feynman diagrams and perturbation theory.
Relative to electrons, muons have a larger mass, thus causing them to orbit closer to the nucleus in a hydrogen-like atom. For a muon in a uranium ion, with an atomic number of Z = 92, the radius of the orbit can be calculated using modified Bohr model equations accounting for the larger mass of the muon.
Experimentally, muon magnetic moments are determined through precision measurements of their behavior in magnetic fields, and these results are then used to refine theoretical models.
The electron magnetic moment is significantly larger than the muon magnetic moment due to the mass difference. In the case of the same state of orbital angular momentum, the ratio of their magnetic moments is directly related to their mass ratio, which is 1/207.
Specifically, for an electron in the 3p state (n = 3, l = 2), the orbital magnetic dipole moment would be expressed in terms of the Bohr magneton (μB).