Magnetic effect in the test of the weak equivalence principle using a rotating torsion pendulum

The high precision test of the weak equivalence principle (WEP) using a rotating torsion pendulum requires thorough analysis of systematic effects. Here we investigate one of the main systematic effects, the coupling of the ambient magnetic field to the pendulum. It is shown that the dominant term, the interaction between the average magnetic field and the magnetic dipole of the pendulum, is decreased by a factor of 1.1 × 10⁴ with multi-layer magnetic shield shells. The shield shells reduce the magnetic field to 1.9 × 10^-9 T in the transverse direction so that the dipole-interaction limited WEP test is expected at η ≲ 10^-14 for a pendulum dipole less than 10^-9 A m². The high-order effect, the coupling of the magnetic field gradient to the magnetic quadrupole of the pendulum, would also contribute to the systematic errors for a test precision down to η ∼ 10^-14.