When a steady current flows in a metallic conductor of non-uniform cross section, which of these quantities is constant along the conductor?
A. Current
B. Electric field
C. Drift speed
D. Current density
E. Potential gradient
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → A Only
A steady current means that charge does not pile up anywhere in the conductor. By conservation of charge, the same charge must then cross every cross-section each second, whatever its area. The other quantities all depend on the area \( A \) of the cross-section:
\( J = I/A \)
\( E = J/\sigma = I/(\sigma A) \)
\( v_{d} = I/(n e A) \)
(A) Current — Correct. The same charge flows through every cross-section per second in the steady state, so the current is the same along the whole conductor.
(B) Electric field — Incorrect. From \( J = \sigma E \), the field is \( I/(\sigma A) \), so it is stronger at the narrow parts and weaker at the wide parts.
(C) Drift speed — Incorrect. From \( I = n e A v_{d} \), the drift speed varies inversely with the area: the electrons move faster through the narrow parts.
(D) Current density — Incorrect. Current density is current per unit area, \( J = I/A \), so it changes wherever the area changes.
(E) Potential gradient — Incorrect. The potential gradient is equal in magnitude to the electric field, so it varies with the area in the same way as the field in (B).
NCERT (2026-27):
Kirchhoff’s Rules – “… (a) Junction rule: At any junction, the sum of the currents entering the junction is equal to the sum of currents leaving the junction (Fig. 3.15). This applies equally well if instead of a junction of several lines, we consider a point in a line. The proof of this rule follows from the fact that when currents are steady, there is no accumulation of charges at any junction or at any point in a line.”