Classical Electrodynamics 3rd. edn

Mathematics of Classical and Quantum Physics Books on Physics) Publication

Throughout this text we use the Einstein summation convention: repeated Greek indexes are summed from 0 to 3, latin indexes are summed over from 1 to 3, and we use the natural unit system as well unless explicitly stated otherwise

In the case of the vector potential, ρ is replaced by j

The l-th Legendre Polynomial is Pl (z) = 1 2ll! dl dzl z2 - 1 l

Notice that condition (37) is, in fact, a consequence of conditions (38) and (39)

Of course, ϕ(0) is dominant as long as the monopole term is nonvanishing

is the Heaviside step function defined as Θ (x) = 1 if x ≥ 0 and Θ (x) = 0 otherwise

Here, ri is the i-th component of the vector r

As usual, r ∈ [0, ∞), θ ∈ [0, π], and φ ∈ [0, 2π)

In plotting figure (4), we set mP = 1 and I = 1