= Solution
With the left reservoir at $V$ and the right at zero, let the pore run from $x=0$ to $x=\ell$. In the stated idealization the reservoir potentials are flat, the pore potential is $\phi(x)=V(1-x/\ell)$, and its electric field is \b[$E_x=-d\phi/dx=V/\ell$], directed from high to low potential. The field is zero in the ideal equipotential reservoirs; real access regions would round these abrupt boundaries.
\Image[/past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2017/paper-2-pore-signals.png]
{title=Ideal potential, field and current blockade for a generic insulating particle crossing a uniform pore}
{source=paper-2-pore-signals.py}
For constant-speed passage and an approximately position-independent in-pore obstruction, the current has a rectangular downward pulse from $I_0$ to $I_0-\Delta I$ during occupation. Entry, exit, filtering and nonuniform fields round real pulses. This describes a physical particle signal without inferring any biological identity or charge.
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