= Solution
For the <theta pinch>, the <electric current> is azimuthal:
$$
\mathbf j_0=\frac c{4\pi}\nabla\times(B_0\hat{\mathbf z})=-\frac{cB_0'}{4\pi}\hat{\boldsymbol\theta}.
$$
Its <Lorentz force> is $\mathbf j_0\times\mathbf B_0/c=-B_0B_0'\hat{\mathbf r}/(4\pi)$. Static radial balance with the <pressure> gradient therefore gives
$$
\boxed{p_0'+\frac{B_0B_0'}{4\pi}=0,\qquad p_0(r)+\frac{B_0(r)^2}{8\pi}=\text{constant}.}
$$
The constant is the equilibrium <magnetohydrodynamic total pressure>.
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