### Current Density Formula, equation With Example.

The current density J_{(A/m}^{2}_{)} in Ampere per square meter is equal to the flow of current I_{(A)} in Amps divided by the cross section area A_{(m}^{2}_{)} of the conductor in square meter. Hence the formula can be written as

J_{(A/m}^{2}_{) } = I_{(A)} / A_{(m}^{2}_{)} —————————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/m}^{2}_{) } = Q _{(C)} / (A_{(m}^{2}_{)} x t_{(s)})

Also, current density J_{(A/m}^{2}_{) } is the product of charge density ρ in C/m^{3} and the velocity of the electron in m/s. Therefore the formula can be written as,

J_{(A/m}^{2}_{) } = ρ _{(C/m}^{3}_{)} 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/m^{2}

Current density = 4 A/m^{2}

### Current density thumb rule:

A copper conductor 1 Sqmm carries 1.7 A/mm^{2}, In case for bus bar, the cu conductor carries only 1.2 times of the area.

A Aluminum Conductor carries 1 A/mm^{2}. AL busbar carries only 0.8 times of the cross section.