I have troubles with solving this integral, the only thing I know is that
$VI\dfrac{L}{\mu}\oint_{ch}\phi\nabla_t\phi\cdot \mathbf{\nu}\,\,dl$
= V*I * $\frac{L}{\mu}* \frac{C}{\epsilon}$, which means that the integral part must be equal to $\frac{C}{\epsilon}$. Additional to this, it is known that $\frac{C}{\epsilon}=\oint_{ch}-\nu\nabla_t\phi\cdot \,dl$
My question is how to get from the first integral to the second, while it is known that $\phi(Q) = 1 $ and $\phi(P) = 0 $ where P and Q are points on the contour