TransWikia.com

Definition of current density

Physics Asked by fierydemon on August 28, 2021

In David Tong’s lectures on Electromagnetism, the current density is defined as $vec J=qrho vec v$, where $rho$ is the density of particles with charge $q$, and $vec v$ is the average velocity. This should be the area density, and not the volume density right? It seems that Tong is assuming that this is the volume density of charges.

2 Answers

The current density is defined by the current per unit area. If you multiply by the area (being crossed) you get the total current. In this case if you multiply the charge density by velocity (distance / time), you get the charge which will cross the unit of area in a unit of time.

Answered by R.W. Bird on August 28, 2021

The equation is correct except that usually it is written $vec J=rho vec v$ where $rho$ is the charge density instead of the number density. So I will use the standard expression.

The SI units of $rho$ are $text{C}/text{m}^3$ which looks like it will give a volume density. But the units of $vec v$ are $text{m}/text{s}$ so the overall units of $vec J$ are $text{C}/text{m}^2text{s}$. Thus, the formula indeed gives an area density, meaning the current density integrated over an area gives the current flowing across that area.

Answered by Dale on August 28, 2021

Add your own answers!

Ask a Question

Get help from others!

© 2024 TransWikia.com. All rights reserved. Sites we Love: PCI Database, UKBizDB, Menu Kuliner, Sharing RPP