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Q. A steady current flows in a metallic conductor of non-uniform cross-section. The quantity/ quantities constant along the length of the conductor is/are

Solution:

If $E$ be electric field, then current density $j=\sigma E$
Also we know that current density $j=\frac{i}{A}$
Hence $j$ is different for different area of cross-sections.
When $j$ is different, then $E$ is also different. Thus $E$ is not constant.
The drift velocity $v_{d}$ is given by $v_{d}=\frac{j}{n e}=$ different for different $j$ values.
Hence only current $i$ will be constant.