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.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$\rho (r)\, = \,{\rho _0}\left( {1 - \frac{r}{R}} \right)$ for $r < R$
$\rho (r)\,=\,0$ for $r\, \ge \,R$
Where $r$ is the distance from the centre of the charge distribution $\rho _0$ is a constant. The electric field at an internal point $(r < R)$ is
