We generalize the derivation of electromagnetic fields of a charged particle moving with a constant
acceleration Singal (2011 Am. J. Phys. 79 [http://dx.doi.org/10.1119/1.3620257] 1036 ) to a variable
acceleration (piecewise constants) over a small finite time interval using Coulomb’s law,
relativistic transformations of electromagnetic fields and Thomson’s construction Thomson (1904
Electricity and Matter (New York: Charles Scribners) ch 3). We derive the average Lorentz self-force
for a charged particle in arbitrary non-relativistic motion via averaging the fields at retarded
time.