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In several studies conducted recently, it was shown that equations pertinent to the electric and magnetic fields produced by electrical charges in motion can be used to calculate the electromagnetic fields produced by current pulses propagating along linearly restricted paths. An example includes the case of current pulses propagating along conductors and conducting channels such as lightning. In this paper, it is shown how the technique can be applied to estimate the electromagnetic fields generated by current and charge distributions moving in arbitrary directions in space. The analysis shows that, depending on the way the problem is formulated using the field equations pertinent to accelerating charges, one procedure leads to the generalized dipole equations, which are independent of the velocity of propagation of the current, and the other procedure leads to a set of equations that depend on the velocity. Using the well-tested transmission line model of lightning return strokes as an example, it is shown that both sets of field equations give rise to the same total electromagnetic field.