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,
KVPY 2018, Advanced
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(b)

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

$\Rightarrow I_1=I_2$

$\Rightarrow j_1 A_1=j_2 A_2$

$\Rightarrow \frac{j_1}{j_2}=A_2 < 1$

$\Rightarrow A_1$

$\Rightarrow j_1 < j_2$

Current density increases in the narrow region.

$\text { Also, } j=n e v_d$

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

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

Drift velocity increases in the narrow region.

and $\quad j=\frac{E}{\rho}$

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.

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