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Current Density in a Conducting Medium

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

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where I is the current in Amperes and A is the cross-sectional area of conducting medium in metre2. 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.
image electrons carry 1 Coulomb of charge. So the movement of 6.25 × 1018 electrons for 1 s contributes to 1 A of current in a conductor.

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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.

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

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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

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where μ is the mobility of charge carriers.
Current density Jp due to the movement of Holes = pqμpE.

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