Let B(x, z) be the magnetic field produced by a surface current density K(y, z) = K(z) ŷ confined to the x = x₀ plane.

(a) Show that the Biot-Savart law for this situation reduces to a one dimensional convolution integral for each component of B.
(b) Confine your attention to x < x₀ and show that

(c) Why does the single component Bz(x, z) evaluated at one (arbitrary) value of x < x₀ provide enough information to determine j (z)?

Transcribed Image Text:

μοΚ (2) - ² Ĵ az Ĵ dk dz' = 88 -∞ f dk exp{ik(zz) + k|(xox)} B₂(x, z).