The units for current density don't check out

[CraigH]

In my lectures the equation for current density was given as:

$J=n*q*vd$

where:
n = the number of electrons per unit area
q = electron charge
vd = drift velocity of electrons

If you rewrite this equation as:

$J=\frac{N}{A}*q*\frac{dr}{dt}$

where:

$\frac{N}{A}$ is the number of electrons per unit area

and

$\frac{dr}{dt}$ is the distance each electron moves per second. ie. The drift velocity.
(this distance ignores the distance the electrons move due to their random thermal velocities. This is the distance that they all move together due to the electric field)

Now...

$J= \frac{I}{A}$

$\frac{I}{A}=\frac{N}{A}*q*\frac{dr}{dt}$

$I =N* q*\frac{dr}{dt}$

N * q is the total charge

$I =Q*\frac{dr}{dt}$

So the units for electrical current are coulomb meters per second.

However I know this is not true. The units of current are coulombs per second.

In the actual equation for current why is there no distance involved? I understand that you can model each coulomb as a particle, and then the current is a flow rate, ie. the number of particles per second. But when you try and derive this from current density it doesn't work out.

Will someone please explain how you can get from the current density equation, to the actual equation for current?

(the "actual equation for current" being $I=\frac{dQ}{dt}$)

Thanks!

 

[CraigH]

Also, I've just checked the current density equation:

J = nqv

and it is definitely correct. It is also given on this website http://physics.info/electric-current/

 

[jtbell]

n = the number of electrons per unit area

No, it's the number of electrons per unit volume.

 

[CraigH]

Ah okay, yeah that makes sense. It must have just been a typo in my lecture slides.
Thanks

 

[sardar]

It is important to note that the equation for current density (J=n*q*vd) is a simplified version that assumes a uniform flow of electrons in a specific direction. In reality, the movement of electrons is much more complex and can involve both a drift velocity and a random thermal velocity.

The equation for current density does not take into account the distance that the electrons move due to their random thermal velocities, as this movement is considered negligible compared to the drift velocity. Therefore, the equation for current density does not include a distance term.

To understand the relationship between current density and current, we can start with the definition of current as the rate of flow of charge (I=\frac{dQ}{dt}). This means that the current is equal to the change in charge over time. In the case of a uniform flow of electrons, the number of electrons per unit area (N/A) can be substituted for charge (Q), and the drift velocity (vd) can be substituted for the distance (dr/dt).

This results in the equation I=N*q*vd, which is equivalent to the equation for current density (J=n*q*vd). However, when we consider the actual movement of electrons, the equation for current must take into account the random thermal velocities of the electrons as well. This is why the equation for current (I=\frac{dQ}{dt}) does not include a distance term.

In summary, the equation for current density is a simplified version that assumes a uniform flow of electrons, while the equation for current takes into account the more complex movement of electrons. Both equations are valid in different contexts and can be derived from each other by making certain assumptions and simplifications.