Radiation Recoil Problem for Classical Charged Dust Grains

We consider several classical problems (Coulomb scattering, motion in a constant external electromagnetic field, Brownian motion) for the Sommerfeld model of an extended charged particle (“dust grain”). We find essential differences from the classical result in both quantitative aspects (a change of the angle in Coulomb scattering, decrease of the diffusion coefficient for a Brownian particle, deceleration of outspiraling of the “dust grain” in a cyclotron) and in qualitative aspects (occurrence of the tunneling effect through a potential barrier). These differences do not disappear as the size of the particle tends to zero. The equation of motion of an extended object therefore does not have a smooth limit transition to the Newton equation for a point.