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**Current Density and Drift Velocity**

The current flowing through a unit cross-sectional area of a conductor is called **current density (J)**.

Current Density and Drift Velocity |

**Mathematically**, If '

**dI**' current passes through a cross-sectional area ‘

**dt**’ of a conductor then

**current density**may be written as

**Current Density**= J = dI/da ➔ 1

If the

**current**is measured in ‘

**Ampere**and

**area**in ‘

**meter**’ then

**J**= Amphere/(meter)² = A/m²

**J**= Am⁻²

**The unit**of current density is Am⁻².

From Equation 1, we can write

**J**= dI/da ⇒ dI = Jda ➔ 2

**Integrating**equation 2

**∫ dI**= ∫ J.da

**I**= J ∫ da

**I**= JA

**J**= I/A

**Current density**is a vector quantity and its direction is the same as that of

**electric field Ē**.

When a conductor is connected to a battery, the free electrons move from low potential to high potential i.e from

**the negative terminal**to the

**positive terminal**.

During motion, the force electrons collide with the ionic cores of the conductor. The

**K.E**of the accelerating electrons is converted into vibrational energy of the lattice the constant average velocity acquired by free electrons against the electric field is called

**Drift Velocity V𝒹**.

It is of the order

**10⁻³ms⁻¹**. In order to calculate the magnitude of

**drift velocity**, let us take a conductor of

**length 'L**' and

**area of cross-sectional 'A'**then the volume of the conductor is equal to

**AXL**.

The volume of the conductor = AXL ➜ 1

If the unit volume of the conductor carries

**n charge**careers then

Total no of charge careers in the conductor =

**n (AXL)**➟ 2

And if each charge career carries a charge

**'e'**then

Total charge on the conductor =

**e [n(AL)]**

q = e (nAL) ➜ 3

When this conductor is connected to a voltage source, the charge careers will start to flow from the negative terminal to the positive terminal with an

**orbit velocity**

**V𝒹.**

If

**'t'**is the time taken by the charge careers to pairs through the whole

**length (1)**of the conductor then we can white.

**S**= v x t

**L**=

**V𝒹 x t**

**t =**L/V𝒹 ➜ 4

Due to the motion of these charge careers, a

**current 'I'**will be established whose magnitude is given as

**I**=q/t ➜ 5

Putting the value of

**q**and

**t**from

**equations 3 and 4**into above equation 5 we have

**I**= e (nAL) / L/V𝒹

**I**= e (nA)V𝒹

**V𝒹**= I/ (nA)e

**V𝒹**= I/A x 1/ne

**V𝒹**= J x 1/ne ➜ 6

The above equation correlates the drift velocity with

**current density**. Since the moving charge careers in a conductor are electrons so the above equation can be rewritten as

**V𝒹**= J / (-e)n

**J**= en (-V𝒹)

Thus the direction of

**drift velocity and current density**are opposite to each other.

**Editors Recommendations:**

Current Density and Drift Velocity
Reviewed by AB Ultimate Guides
on
July 12, 2020
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