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In this question, I am unable to understand why charge would pile up at the junction in the first place. This is current electricity, not electrostatics, and the current is same through both the materials, obviously. So, the charge flowing in would be the same as the charge flowing out. Where am I going wrong with this logic? I do not want the answer to this particular question, just a push in the right direction would suffice.

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  • $\begingroup$ The pile up would occur even if there is no current: it is a consequence of the different chemical potentials in the two materials. $\endgroup$
    – Roger V.
    Commented Oct 23, 2020 at 10:16

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The accumulation is due to difference in electric field at two points .HINT try relating flux and electric field for charge accumulation

${E} = \frac{J}{\sigma}$ where $j$ is the current density and ${\sigma}$ is conductivity

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