Verify that the current carried in electro-osmotic flow can be expressed as [I=int_{0}^{R} 2 pi r v_{z}

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Verify that the current carried in electro-osmotic flow can be expressed as

\[I=\int_{0}^{R} 2 \pi r v_{z} ho_{\mathrm{c}} d r\]

Using this relation, derive an expression for the current in electro-osmotic flow.

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