# Current Density In A Conducting Medium

Currents in metals are due to the movement of charge carriers ‘electrons’.

where *I* is the current in Amperes and *A* is the cross-sectional area of conducting medium in metre^{2}. Describing current density *J *as current per unit area has the advantage, since the dimensions of the conducting medium are not directly involved. Relation between current density and charge density *ρ* is described in the following:

**Current density:** Current *I* (Amperes) through a conductor by definition is *Charge* (in Coulombs)/*Time *(in seconds). Current is due to the movement of charges through a conducting medium in a given time. If, 1 C of charge moves through a conducting medium in 1 s, the resulting *current* is 1 A.

electrons carry 1 Coulomb of charge. So the movement of 6.25 × 10^{18} electrons for 1 s contributes to 1 A of current in a conductor.

where *q* is the charge of an electron and *N* is the number of electrons in a given volume. If the charge passes through a distance *L* (metres) in time *T* (seconds), through a conducting medium, then the velocity *v* with which the electrons move is *L*/*T*.

Substituting the value of *T* from Eq. (2.13) in Eq. (2.12), we get

where *n* = *N*/*AL* is the concentration of electrons that is the number of electrons per unit volume.

Using *v* = *μE* in Eq. (2.16), we get

where *μ* is the mobility of charge carriers.

Current density *J*_{p} due to the movement of Holes = *pqμ*_{p}*E.*