Physics · Current Electricity · NEET
Current I is a scalar, but current density J is a vector. J points in the same direction as the electric field E inside the conductor (the direction positive charge would move). This is why the vector form is written J = sigma E. Note: even though J is a vector, when it flows across an area, the current I = J·A is a scalar dot product, so I can be positive or negative depending on the angle.
Current I is the total charge crossing a section per second (unit: ampere, A). Current density J is that current spread over the area, i.e. current per unit area (unit: A/m²). Same current I in a thin wire gives a much larger J than in a thick wire, because the area A is smaller. So J depends on the wire's thickness while I does not.
Ampere per square metre, written A/m². It comes straight from J = I/A: ampere divided by metre squared. Do not confuse it with A/m (that is the unit of magnetic field intensity H, a different quantity).
Inside a conductor, E = J·rho and equivalently J = sigma·E, where rho is resistivity and sigma = 1/rho is conductivity. This is the microscopic form of Ohm's law. It is more fundamental than V = IR because it holds at every point inside the material, not just for the whole conductor.
Current I is a bulk value for the whole wire. Current density J describes what happens at a point inside the material, so it can vary from point to point. It links directly to E, drift velocity (J = n·e·v_d) and conductivity, which is why NEET numericals on drift and Ohm's microscopic law all use J.
A copper wire of length 10 m and radius (10^-2 / sqrt(pi)) m has resistance 10 ohm. The current density for an electric field strength of 10 V/m is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
It is the current flowing per unit cross-section area taken normal to the flow: J = I/A.
J = I/A for the magnitude, and the vector form J = sigma E, where sigma is conductivity and E is the electric field.
For a uniform wire carrying steady current it is the same across the section, but if the wire changes thickness, J is larger where the area is smaller since I stays the same.
J = n·e·v_d, where n is the number of free electrons per unit volume, e is electron charge and v_d is drift velocity. So J is proportional to drift velocity.
Because it links field E and current density J at every point inside the material, unlike V = IR which only relates whole-conductor values.
