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Potential Jump Condition

The potential jump condition defines a discontinuous electric potential \(\phi\) with a given difference in value at the boundary of two contacting regions:

\[\left. \phi \right|_{\partial\Omega_1} - \left. \phi \right|_{\partial\Omega_2} = \phi_0,\]

where \(\partial\Omega_1\) and \(\partial\Omega_2\) are the touching boundaries of the two regions and \(\phi_0\) is the desired value of the electric potential jump.