Many of the answers given above are wrong. The word "causal" is not subjective. One of the answers includes the analogy:
if I (the charge) throw a ball (the electric field) at a lamp, was the cause of the lamp breaking (the change in the magnetic field) the ball or me?
But this is not a good analogy because the two cases are not at all similar. If a charge oscillates and produces a change in a magnetic field, there is a time reversed version of the process that can and does happen. This is not just a theoretical possibility, it is the sort of thing that people can in fact do in a lab. So there is a sense in which it is not clear which event is a cause and which is the effect. Causality between charges and fields can sometimes be made clear in the context of a specific explanation. For example, if you have a transmitter, you can control the charges in the transmitter and produce a field as the effect of controlling those charges. If you have an aerial you don't control the field around the aerial, the field around the aerial controls the signal produced by the aerial. But if all you have is a description of oscillating fields and charges in general you can't work out which is cause and which is effect.
There are several disanalogies between the ball and the fields. Throwing the ball at the lamp is not time reversible. Anyone who claims that it is time reversible is playing a word game that has nothing to do with the sorts of operation that can be done in reality. There is an objective sense in which the lamp would not break if the ball was not thrown. And there is an objective sense in which the lamp breaking is the effect and not the cause. And there is an objective sense in which the ball being thrown is the cause and not the effect.
Part of the problem people have with understanding cause and effect is that causality is a relatively high level abstract issue compared with equations of motion. Generally, cause and effect have to be judged in the context of an explanation of what has happened. You can't just crank the wheel on an equation of motion and have the right answer pop out.
Now, the electric and magnetic fields in a region can change without the charges in that region changing, so if you can't think in terms of electric and magnetic fields you're in trouble. Also, even in many cases where electric and magnetic fields interact with a material, and so interact with charges, it is possible and useful to treat what's going on without explicitly taking account of the charges. For example, reflection and refraction at the surface of a dielectric can be treated in terms of continuity of fields. There is an underlying explanation of refractive index etc. in terms of fields interacting with charges, but once you know that explanation you don't have to treat it explicitly in every case and doing so will get in the way of understanding.
One of the answers claims that we can't know that causality exists because we can't directly observe it according to Hume. The same answer also claims that we arrive at ideas by inference from experience, but this is false. (Another answer claims that we inductively verify ideas, which is another name for the same alleged process and is also false and extremely misleading.) For example, for a lot of observations of the motion of the solar system made before the 19th century, general relativity and Newtonian mechanics agree on their predictions. So there can't be a right way of inferring the right theory from observations since we have two contradictory explanations of the same events.
We know about the causal connection between two events in the same way we know about anything else. We guess about the solution to some problem, then we criticise the guesses until only one is left and it has no known problems. Our knowledge is not based on anything at all. It is guesswork controlled by criticism including results of experiments. See, for example, "Realism and the Aim of Science" by Karl Popper, Chapter I, which has a section refuting Hume. "Objective Knowledge" by Popper Chapter 1 refutes the idea that theories are inferred from experience. See also "The Fabric of Reality" by David Deutsch, Chapters 3 and 7. "The Beginning of Infinity" by Deutsch, Chapters 1,2,5 is also worth reading, especially chapter 5 part of which treats the issue of causality.