Are longer and shorter DNA similarly charged?
Each phosphate group has a single negative charge. Not just the terminals. The reason gel electrophoresis works so well with DNA is that charge is linearly proportional to size. The longer the fragment, the slower it moves. A double stranded DNA molecule with 100 nucleotides has a charge of -200. If it were twice as long, it would have twice as many, just as if it were 3.4 times longer, it would have 3.4 times as many negative charges. This way, charge is essentially ignored, so DNA migrates through the gel at a rate inversely proportional to its size.