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(B) For a metallic conductor, the total current $I$ flowing through any cross-section must be the same due to the principle of conservation of charge

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(B) For a metallic conductor, the total current $I$ flowing through any cross-section must be the same due to the principle of conservation of charge (steady state flow).Since $I = nAev_d$ and $J = I/A = nev_d$, if the cross-sectional area $A$ varies, the current density $J$ and drift velocity $v_d$ must also vary to keep $I$ constant.The electric field $E = J/\sigma$ also varies with the cross-sectional area.Therefore, the current $I$ is the only quantity that remains constant along the conductor.

Across a metallic conductor of non-uniform cross-section, a constant potential difference is applied. The quantity which remains constant along the conductor is

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