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, $j=ne{v}_d$

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

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

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