Current Density Formula, Equation, Derivation, Example

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Current Density Formula, equation With Example.

The current density J(A/m2) in Ampere per square meter is equal to the flow of current I(A) in Amps divided by the cross section area A(m2) of the conductor in square meter. Hence the formula can be written as

J(A/m2)  = I(A) / A(m2) —————————1

Or

Current density = Current / cross section are of the conductor

Also, by considering the of current is the rate of flow charges means, the current density formula will be

Amps = charge / seconds

I = Q / t

Hence the current density is equal to the ratio of charges Q in coulomb to cross section area times of the timing in seconds. The formula will be,

J(A/m2)  = Q (C) / (A(m2) x t(s))

Also, current density J(A/m2)  is the product of charge density ρ in C/m3 and the velocity of the electron in m/s. Therefore the formula can be written as,

J(A/m2)  = ρ (C/m3) x v (m/s)

Apply the microscopic current I in amps is equal to the number of electron times of area of the conductor and the velocity of the electron.

I = nqAv ————————2

Apply equation 1 in 2, then current density formula will be

J = nqv.

Hence the microscopic current density is equal to the particle density times of the velocity of the electron.

Example:

Calculate the current density of the 2.5 sqmm cross section conductor carries 10 mA per second.

Apply our formula 1,

J = 10 x 10-3 / 2.5 x 10-3

J = 4 A/m2

Current density = 4 A/m2

Current density thumb rule:

A copper conductor 1 Sqmm carries 1.7 A/mm2, In case for bus bar, the cu conductor carries only 1.2 times of the area.

A Aluminum Conductor carries 1 A/mm2. AL busbar carries only 0.8 times of the cross section.

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