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Current Density

Before we discuss current density, it’s necessary to know about electric current. Electric current is defined as the amount of electric charges passing through a unit cross sectional area of the conductor in a unit time. It means electric current is produced due to the flow of electric charges. The branch of electricity that studies the process associated with the flow of current is called current electricity.

Electric charges are conserved that means it is neither created nor destroyed at any point in the conductor. Suppose the electric charge Δ
Q flow through any cross-sectional area of the conductor in time interval Δt, then the average electric current I flowing is given as:

I = ΔQ / Δt

Unit of electric current = ampere (A)

The rate of flow of the electric charge passing through different cross-sectional area of conductor may not be same all the time and the flow of the electric charge may not be perpendicular to the cross-sectional area of the conductor. Let us consider point P of the curved cross-sectional area of the conductor and Δ
a is the area of the surface near point P. Then the current density (J) is given as:
J = ΔI / Δa · cosø

Current density is defined near any point is defined as the amount of electric current flowing perpendicularly to the unit cross-sectional area near that point.

The current density can also be expressed as:

J = N · q · u

Since the current is given by:
Δ
I = ΔQt = N · q · u · an · Δs = N · q · u · Δs

Where:
N is the number of charge carries per unit.
q is the charge each one carries.

u is the velocity the charges has when they move across the surface Δs, which has a unit normal an.
Δ
t is the time variation.

Since
N · q = ρ, the current density can also be expressed as:
J = ρ · u

Example: Match the following properties:
(A)
Electric current 
Current density 
Current electricity 
Electric charge

(B)
Branch of electricity that studies electric current
neither created nor destroyed
Electric charge flowing in a unit time
Motion of electric charges

Electric current → Motion of electric charges
Current density → Electric charge flowing in a unit time
Current electricity → Branch of electricity that studies electric current
Electric charge → neither created nor destroyed



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