That's a pretty neat video, I'll just give you some background information first. It's an illustration of the "trombone model" of DNA replication. The darker blue molecule is helicase, it unwinds the DNA and facilitates translocation (this is an ATP dependent process). The dark purple molecules are DNA polymerase, they catalyze DNA strand synthesis (an NTP dependent process) using an ssDNA template and 3'-OH primer (the primer:template junction). The green circular molecules are sliding clamps, they increase the processivity of DNA polymerase. The light purple molecule is the sliding clamp loader, unsurprisingly it loads the sliding clamp onto the DNA (ATP dependent). The light blue molecule is a flexible linker that connects everything together. The other green molecule (the one that contacts helicase) is primase, it synthesizes RNA primers (which contains the 3'-OH initially used by DNA polymerase).
Certainly intermolecular forces play a significant role in this (and every) biochemical process, but I'm not really sure what you're talking about when you're describing electric forces and Brownian motion.
Anyways, the answer to your question is no, Okazaki fragments do not have a fixed length. DNA synthesis, as mentioned above, occurs only by adding NTPs to a 3'-OH primer. Thus the length of Okazaki fragments is dependent on the spacing between primers on the lagging strand. This is dependent on when primase binds which in turn is dependent on primase concentration as well as its binding affinity with DNA and other replication fork proteins (especially helicase). High concentration and/or high affinity leads to a higher binding frequency and therefore shorter Okazaki fragments. The opposite is true for low concentration and/or low affinity. Note that most (or all?) primases have some degree of sequence specificity which means that specific DNA motifs will increase binding affinity. For example, Escherichia coli primase (DnaG) recognizes the trimer GTA.
This process also requires some degree of coordination between leading and lagging strand synthesis. Primer synthesis and DNA polymerase recycling on the lagging strand is much slower than the continuous synthesis on the leading strand. It has been suggested that primase acts as a "molecular brake" by halting the replication fork during primer synthesis to prevent the leading strand polymerase from rapidly outpacing those on the lagging strand (Lee JB, Hite RK, Hamdan SM, Xie XS, Richardson CC, van Oijen AM. 2006. DNA primase actas as a molecular brake in DNA replication. Nature. 439(7076):621-624.).