= Cylindrical magnetostatic pressure balance
For an <axisymmetric vector field> independent of the axial coordinate and regular on the axis, <Gauss's law for magnetism> gives $B_R=0$. The magnetostatic <Ampère-Maxwell equation> then gives $j_R=0$, $j_\phi=-cB_z'/(4\pi)$, and $j_z=c(RB_\phi)'/(4\pi R)$ in Gaussian units. Radial <magnetostatic equilibrium> is
$$
\frac d{dR}\left(p+\frac{B_z^2+B_\phi^2}{8\pi}\right)+\frac{B_\phi^2}{4\pi R}=0.
$$
For enclosed axial <electric current> $I(R)$, the magnetostatic <Ampère-Maxwell equation> gives $B_\phi=2I/(cR)$, hence
$$
\frac d{dR}\left(p+\frac{B_z^2}{8\pi}\right)
+\frac1{2\pi c^2R^2}\frac{dI^2}{dR}=0.
$$
The first term contains <pressure> and axial <magnetic pressure>; the second combines toroidal <magnetic pressure> with the hoop force from <magnetic tension>.
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