(a) One way to fill in the “missing link” in Fig. 5.48 is to exploit the analogy between...

(a) One way to fill in the “missing link” in Fig. 5.48 is to exploit the analogy between the defining equations for A (viz. ∇ · A = 0, ∇ × A = B) and Maxwell’s equations for B (viz. ∇ · B = 0, ∇ × B = μ₀J). Evidently A depends on B in exactly the same way that B depends on μ₀J (to wit: the Biot-Savart law). Use this observation to write down the formula for A in terms of B.

(b) The electrical analog to your result in (a) is

Derive it, by exploiting the appropriate analogy.

Figure 5.48