How do you derive the drift velocity equation [tex]I = nAve[/tex]?
Answer (3)
current is just number of electrons (times its charge) passing by in a given time (in seconds for amps).
say you have a volume filled with moving electrons (ignore the inner shell electrons since they stay put) if this volume is constantly moving, the current is just the total charge of this moving volume divided by the total time it takes to pass a certain surface. total charge is e n A L where l is the length (this is just total volume charge density*charge/electron) the time it takes this to move a distance L is the time for all the charges to move across some 'measuring' surface, time=distance/velocity=L/v
Current=total charge/total time=enAL/[L/v]=nAve
this is one way to think about it... I hope I helped! ☺️
The **drift velocity **equation, I = nAv_e, relates the current (I) in a conductor to the charge carrier density (n), cross-sectional area (A), and the drift velocity (v_e) of the charge carriers.
To derive this equation , let's start with the basic definition of electric current:
I = Δ Q /Δ t ,
where I represents the current , ΔQ is the charge passing through a cross-sectional area A of the conductor in a time** interval** Δt.
Next, consider a conductor with charge carriers (such as electrons) moving through it. These charge carriers experience collisions with atoms or impurities in the material, causing them to change direction randomly and move with an average drift velocity v_e in the opposite direction to the** electric field.**
The charge passing through the conductor can be expressed as the product of the** charge **carrier density (n), the volume of the conductor (AΔx), and the charge of each carrier (e):
ΔQ = n(AΔx)e,
where Δx is the distance the charge carriers move in the time interval Δt.
We can rearrange this equation to express Δx in terms of the drift velocity v_e and Δt:
Δx = v_eΔt.
Substituting this into the previous equation, we have:
ΔQ = nAv_eΔte.
Finally, substituting ΔQ into the current equation, we get:
I = n A v e Δ t e /Δ t .
Canceling out the Δt terms, we arrive at:
I = nAve.
This equation relates the current I to the charge carrier density n, cross-sectional area A, and drift velocity v_e. It is known as the drift velocity equation.
Learn more about **velocity **on:
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The equation I = n A v e relates current to charge carrier density, cross-sectional area, and drift velocity. By defining current and analyzing the movement of charge in a conductor, we arrive at this important relationship. This understanding is essential in fields involving circuits and electrical properties of materials.
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