Let us imagine a charge $q$ in space. At each point in space,there is an electric field vector associated with it. Now we start moving the charge in a direction. We know that electromagnetic influences travel at the speed of light $c$ and hence fields far away couldn't undergo any change in electric field vector. Here is where I am facing a bit problem.
According to coulombs law,the electric field is given by $\frac{kq}{r^2}$. So,at each point in time,the electric field with vary with the distance $r$ from the source charge will vary both in magnitude and direction. So electric field at each point in space will change in direction and magnitude with the varying position of the source charge. So,is there any error with coulombs law since we know fields far away can't be affected due to electromagnetic influences but coulombs law doesn't seem to take that into consideration and it suggests that fields will keep changing no matter how far the points are?
I am greatly struggling in this topic and this is hindering me from understanding electromagnetism. Kindly shed light on this topic.
