# Current Density (J)

Current density at any point inside a conductor is defined as a vector having magnitude equal to current per unit area surrounding that point. Remember area is normal to the direction of charge flow (or current passes) through that point.

- Current density at point
*P*is given by**Fig. 3** - If the cross-sectional area is not normal to the current, but makes an angle
*θ*with the direction of currentm then*di*=*JdA*cos*θ* - If current density is uniform for a normal cross-section , then
*J*=*i*/*A*. - Current density is a vector quantity. Its direction is same as that of . Its SI unit is amp/m
^{2}and dimension [*L*^{–2}*A*]. - In case of uniform flow of charge through a cross-section normal to it as
*i*=*nqvA*ﬁ*J*=*i*/*A*=*nqv*.**Fig. 4** - Current density relates with electric field as , where σ = conductivity, and
*ρ*= resistivity or specific resistance of substance.