= Poynting flow in resistive parallel strips
{c}
{title2=$\mathbf S=(IV(x)/(ad),0,I^2Rz/(ald))$}
For a resistive upper strip at $z=d$ with $V(x)=V_0-IRx/l$ and an ideal lower strip at zero potential, the narrow-gap approximation gives $\phi=zV(x)/d$ and $\mathbf H=(0,I/a,0)$. The <Poynting vector> has both an axial flux and an upward flux into the lossy conductor. Axial <power> decreases by $I^2R$ along the line, exactly equal to the integrated upper-surface flux. The ideal lower conductor receives no steady dissipation.
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