0
$\begingroup$

In fluids dynamics, I learnt that as rate of flow is constant for an ideal fluid, Area(cross sectional area of the tube) x velocity is constant.I had a doubt whether the same relation exists between drift speed and cross sectional area of conductor.

$\endgroup$

2 Answers 2

1
$\begingroup$

The relation between drift speed and cross sectional area in a conductor with constant current and different cross section is the same as for an incompressible fluid flow in a tube with changing cross section, i.e., $$v_1 A_1=v_2 A_2$$ as long as the charge carrier density $n$ (e.g. electrons in a metal) is constant. This follows from the conduction current continuity for stationary currents: The conduction current $I$ stays constant along the conductor $$I=I_1=A_1 n_1 e v_1=A_2 n_2 e v_2=I_2$$ This follows from the law of charge conservation which in the stationary case reads $$\nabla · \vec j=-\frac {\partial \rho}{\partial t}=0$$ In its integral form this means that the closed surface integral $$\int_{\Sigma} \vec j d \vec a=0$$ where the current density is given by $\vec j=n e \vec v$.

$\endgroup$
1
$\begingroup$

In the case of a pipe, what is conserved is $$\frac{dm}{dt} = \rho A v. $$

In a wire, the current is conserved:

$$\frac{dq}{dt} = nAu $$ where $u$ is the electron drift speed and $n$ is the charge density.

You should look up the Drude model for more information.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.