Electric Current-
Before you go through this article, make sure that you have gone through the previous article on Electric Current.
We have learnt-
- Electric current is the flow of electric charges through a conductor in a preferred direction.
- Quantitatively, it is the amount of charge flowing through the cross-sectional area of conductor per unit time.
In this article, we will learn about current density.
Current Density-
Electric current may be distributed non-uniformly over the surface through which it passes.
Hence to characterize current in greater detail, the concept of current density is introduced.
The current density at any point inside a conductor across an area held perpendicular to the direction of flow of charges is defined as the amount of charge flowing per unit area.
It is a vector quantity having the same direction as that of electric current. |
Case-01:
Consider current I is flowing uniformly and normally through an area of cross-section A as shown-
In this case, the magnitude of current density at any point of this cross-section is given by-
Case-02:
Consider the area A is not perpendicular to the direction of electric current and its area vector makes an angle θ with the direction of current as shown-
Here, the effective area which is perpendicular to the direction of flow of charges is the component of area having area vector = Acosθ.
In this case, the magnitude of current density at any point of this cross-section is given by-
This formula can also be written as-
This is a general relation between electric current and current density.
Characteristics of Current Density-
- It is a characteristic of any point inside the conductor.
- It is more fundamental than electric current as it is area independent.
- Its SI unit is ampere per square meter (Am^{-2}).
- Its dimensional formula is [M^{0}L^{-2}T^{0}A^{1}].
- It is a vector quantity having its direction same as direction of electric current.
Electric Current Vs Current Density-
Electric Current |
Current Density |
It is always defined for an area and not a point. | It is always defined for a point and not an area. |
It is a scalar quantity. | It is a vector quantity. |
It is denoted by the symbol I. | It is denoted by the symbol j. |
Its SI unit is ampere (A). | Its SI unit is ampere per square meter (Am^{-2}). |
Important Note-
In steady state, the electric current flowing through each cross-section of the conductor is same i.e.
I = constant
In other words,
jA = constantOrj_{1}A_{1} = j_{2}A_{2} |
This relation helps to compare the current densities through cross-sections of different areas.
Read the next article on-
Drift Velocity & Relaxation Time
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