- - Unit CURRENT ELECTRICITY Substituting for dx from equation ( . ) in ( . ) = ( A v d dt ) n Total charge in the volume element dQ = (charge) × (number of electrons in the volume element) dQ = ( e )( A v d dt ) n Hence the current I dQ dt ne A d v ( . ) Current density (J) The current density ( J ) is defined as the current per unit area of cross section of the conductor.
J The S.I unit of current density is A m (or) A m – J neA d v (from equation . ) J ne d v ( . ) The above expression is valid only when the direction of the current is perpendicular to the area A. In general, the current density is a vector quantity and it is given by J ne d v Substituting v d from equation ( .
) J n e =− ⋅ τ ( . ) J =− σ But conventionally, we take the direction of (conventional) current density as the direction of electric field. So the above equation becomes J = σ ( . ) where σ τ = ne is called conductivity.
The equation ( . ) is called microscopic form of ohm’s law. When we say ‘battery has no charge’, it means, that the battery has lost ability to provide energy or provide potential difference to the electrons in the circuit. When we say ‘mobile is charging’, it implies that the battery is receiving energy from AC power supply and not electrons.
. . Microscopic model of current Consider a conductor with area of cross section A and let an electric field E be applied to it from right to left. Suppose there are n electrons per unit volume in the conductor and assume that all the electrons move with the same drift velocity v d as shown in Figure .
. Figure . Microscopic model of current dx d dt e