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Current Density Formula

Current density as word itself suggests is the density of current. It is denoted by the symbol J. In the field of electromagnetism, Current Density is the measurement of electric current charge flow in amperes per unit area of cross-section (m²). This is a vector quantity, with both a magnitude scalar and a direction. An electrical current flowing through a solid, and having units of charge per unit time per unit area measured in the direction perpendicular to the flow direction.

It is about how much current is flowing across the given area.


Current Density Formula is given by,
Where I is the current flowing through the conductor given in Amperes
A is the cross sectional area in m2.

Current density formula is useful in finding Current density, total current and total area if any two of these quantities are given. It is expressed in A/m2.

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Current Density Problems

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Problems based on current density are mentioned below:

Solved Examples

Question 1: A copper wire of area 5 mm2 has a current of 5 mA of current flowing through it. Calculate the current density?
Solution:
 
Given: Total Current I = 5 mA,
          Total Area A = 5 mm2
The Current density is given by J = $\frac{I}{A}$
                                                = $\frac{5 \times 10^{-3} A}{5 \times 10^{-3} m}$
                                                = 1 A/m2.
 

Question 2: Calculate the current density if 50 Amperes of current is flowing through the battery in a given area of 10 m2?
Solution:
 
Given: Current I = 50 A,
          Area A = 10 m2
The current density is given by J = $\frac{50 A}{10 m^{2}}$
                                               = 5 A/m2.
 

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