It depends what you mean by "a single source or set thereof". For example, may we take, as a set of sources, charges moving round a circular track at constant speed, equally spaced from one another? If so, consider a point, P, some way from the centre of the track and on its axis (line through the circle centre at right angles to the plane of the circle). At such a point the electric field and magnetic field due to the charges on the track are both directed along the axis and so parallel or antiparallel to each other.
This result is easily obtainable using mainly symmetry. It could be made quantitative using Coulomb's law and the Biot-Savart law and these, in turn, can (with care and time!) be deduced from Maxwell's equations.
Later addition The set-up in the first paragraph could be achieved in practice by spinning a disc (made of an insulator) with a charged edge.