Second adiabatic theory is used to derive an asymptotic expression for the bounce‐averaged rate of kinetic energy change experienced by charged particles trapped in electric and magnetic fields that conserve the first two invariantsMandJof their motion. The restriction that there exists no electric fieldE∥, parallel to the magnetic field, reduces by one order in the adiabatic expansion parameterm/efrom itsE∥≠ 0 value. If in addition the magnetic field arises solely from, and convects rigidly with, the arbitrary motion of a perfectly conducting magnet, we find that is smaller by yet another order inm/e. Our results generalize and confirm the conclusions of Hones and Bergeson who considerE∥= 0 and the special case of a uniformly rotating conducting magnetized sphere with nonaligned rotation and magnetiza