Physics · Current Electricity · NEET
Take a conductor of area A carrying current. Free electrons move with drift velocity v_d. In a small time t, an electron travels a distance v_d·t. So all electrons inside a cylinder of length v_d·t and area A will cross the end face. Volume of that cylinder = A·(v_d·t). If n is the number of free electrons per unit volume, number of electrons crossing = n·A·v_d·t. Each carries charge e, so total charge crossing = q = n·A·v_d·t·e. Current I = q/t = n·A·e·v_d. That gives I = nAev_d.
n = number density of free electrons (electrons per cubic metre, unit per m^3, about 10^28 to 10^29 for metals). A = cross-sectional area of the wire (m^2). e = charge on one electron = 1.6 x 10^-19 C (use magnitude). v_d = drift velocity, the small average speed electrons gain along the wire (a few mm per second). Multiply all four and you get current in amperes.
In I = nAev_d, the terms n, A and e are fixed properties of a given wire and do not change. So I depends only on v_d. If drift velocity doubles, current doubles. This is why raising the applied voltage (which raises v_d) raises the current.
Just rearrange the formula: v_d = I / (n A e). Plug in current I, number density n, area A = pi r^2 for a round wire, and e = 1.6 x 10^-19 C. The answer usually comes out very small, of the order of 10^-4 m/s, which is normal for drift velocity.
Both are correct and connected. Current density J = I/A, so dividing I = nAev_d by A gives J = nev_d. Use J = nev_d when the question talks about current density (per unit area), and I = nAev_d when it talks about total current through the wire.
The relation v_d = I/(nAe) has no length term. For a fixed current, v_d depends only on n, A and e. Length affects resistance and hence how much current flows for a given voltage, but once the current is fixed, drift velocity is set by the cross-section, not the length.
A copper wire of radius 1 mm contains 10^22 free electrons per m^3. The drift velocity for a 10 A current is (e = 1.6 x 10^-19 C):
Match Column-I with Column-II. (A) Drift velocity (B) Electrical resistivity (C) Relaxation period (D) Current density with (P) m/(n e^2 rho) (Q) n e v_d (R) (eE/m) tau (S) E/J
Try the real previous-year questions from this chapter — each with the answer and a full solution.
I = n A e v_d. Current equals number density of electrons times cross-section area times electron charge times drift velocity.
v_d = I / (n A e). Rearrange I = nAev_d to get drift velocity.
For a fixed wire, both rise together. Physically the applied field sets v_d, and v_d sets the current through I = nAev_d, so they are directly proportional.
Very small, usually about 10^-4 m/s (a fraction of a millimetre per second) even for currents of a few amperes, because the electron number density n is huge.
Current density J = I/A = n e v_d. So J = nev_d is the same relation written per unit area.
