Past exam of the mathematics course of the University of Cambridge / 2005 / iii / Paper 75 / 2 / 1 / Solution

For the theta pinch, the electric current is azimuthal:Its Lorentz force is ${\mathbf{j}}_0\times {\mathbf{B}}_0/c=-B_0{B}_0^{\prime }\hat{\mathbf{r}}/(4\pi )$. Static radial balance with the pressure gradient therefore givesThe constant is the equilibrium magnetohydrodynamic total pressure.