Question

A steady current $I$ is set up in a wire whose cross-sectional area decreases in the direction of the flow of the current. Then, as we examine the narrowing region,

• A. the current density decreases in value
• B. the magnitude of the electric field increases
• C. the current density remains constant
• D. the average speed of the moving charges remains constant

Answer 1

Answer: (B)

When current flows through a conductor of tapered cross-section, current flow through every section remains constant

$\Rightarrow I_{1}=I_{2}$
$\Rightarrow J_{1}A_{1}=J_{2}A_{2}$
$\Rightarrow \frac{j_{1}}{j_{2}}=\frac{A_{2}}{A_{1}}<\,1$
$\Rightarrow j_{1} <\,j_{2}$
Current density increases in the narrow region
Also, $j=nev_{d}$
$\Rightarrow nev_{d_1} <\,nev_{d_2}$
$\Rightarrow v_{d_1}<\, v _{d_2}$
Drift velocity increases in the narrow region
and $j=\frac{E}{\rho}$
where, $\rho$ = resistivity of material
$\Rightarrow \frac{E_{1}}{\rho}<\frac{E_{2}}{\rho}$
$\Rightarrow E_{1}<\,E_{2}$
Electric field magnitude increases in the narrow region