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,


 

 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,
$=ne{v}_d$

$\Rightarrow ne{v}_{d_1}<ne{v}_{d_2}$

$\Rightarrow v_{d_1}<v_{d_2}$

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.