Ω). The earlier time t′ is called the retarded time, and calculated as There are a few notable things about A and ϕ calculated in this way: The Lorenz gauge condition: is satisfied. The position of r, the point at which values for ϕ and A are found, only enters the equation as part of the scalar distance from r′ to r. The direction from r′ to r does not enter into the equation. The only thing that matters about a source point is how far away it is. The integrand uses retarded time, t′. This simply reflects the fact that changes in the sources propagate at the speed of light. Hence the charge and current densities affecting the electric and magnetic potential at r and t, from remote location r′ must also be at some prior time t′. The equation for A is a vector equation. In Cartesian coordinates, the equation separates into three scalar equations: In this form it is easy to see that the component of A in a given direction depends only on the components of J that are in the same direction. If the current is carried in a long straight wire, A points in the same direction as the wire. In other gauges, the formula for A and ϕ is different; for example, see Coulomb gauge for another possibility. Depiction of the A-field See Feynman for the depiction of the A field around a long thin solenoid. Since assuming quasi-static conditions, i.e. the lines and contours of A relate to B like the lines and contours of B relate to J. Thus, a depiction of the A field around a loop of B flux (as would be produced in a toroidal inductor) is qualitatively the same as the B field around a loop of current. The figure to the right is an artist's depiction of the A field. The thicker lines indicate paths of higher average intensity (shorter paths have higher intensity so that the path integral is the same). The lines are drawn to (aesthetically) impart the general look of the A-field. The drawing tacitly assumes , true under one of the following assumptions: the Coulomb gauge is assumed the Lorenz gauge is assumed and there is no distribution of charge, the Lorenz gauge is assumed and zero frequency is assumed the Lorenz gauge is assumed and a non-zero but sufficiently low frequency