Given a test charge, let's say on the vertical y axis. Another charge vertically below it moves past at a significant speed compared to c. From the Lorentz transformations (in most E&M books) the electric field and thus the force on the test charge will be greater than would be the static coulomb force it the moving charge was instead at rest below the test charge. Does this treatment give the total force? I ask because the moving charge is also said to have a magnetic field. A non moving test charge would of-course have no magnetic force on it if it is in a steady magnetic field. But the lower charge is moving by, so wouldn't its magnetic field be moving past the test charge and that moving magnetic field generate an electric field that would affect the test charge? Is this correct? If so, would this be a force in addition to the force mentioned above or does the above E force incorporate it? By-the-way, I took E&M decades ago with the text from Reitz and Milford (yuk). Well I did, Rusty I am.