Question

A steady current flows in a metallic conductor of non-uniform cross-section. The quantity/quantities remaining constant along the whole length of the conductor is/are:
a) current, electric field, drift speed
b) drift speed only
c) current and drift speed
d) current only

Answer 1

The non-uniform cross-section conductor has areas varying at different places for the same current, steady current. By the very definition of current, charges coming in at one end have to move out at the other end at any moment. So, whatever the cross-section, the current remains the same all along.

Complete step-by-step solution:
Metallic conductor of non-uniform cross-section means area is different at different distances because of non-uniformity.
When a steady current goes through a metallic conductor of non-uniform cross-section, then drift velocity ($V_{d}$) and electric field (E) will be-
$V_{d} = \dfrac{I}{neA}$ and $E = \dfrac{I}{\rho A}$
$\implies V_{d} \propto \dfrac{1}{A}$ and $E \propto \dfrac{1}{A}$
Drift velocity and electric field, both are dependent on area.
Only current remains constant.
In a metallic conductor of non-uniform cross-section, only the current remains constant along the whole length of the conductor.
Option (d) is correct.

Additional Information Current density will change inversely with the cross-section. Areas with smaller cross-sections will have more resistance and hence more voltage drop. It takes more effort to push charges through them. Thus, such an area will have more field strength compared with a cross-section of larger areas.

Note: When a steady current flows in a metallic conductor of non-uniform cross-section, the conductor's current flowing is constant. Current does not depend on the conductor area; it remains constant. Current density, drift speed, and electric field are inversely proportionate to the cross-section area.