Question

The drift velocity does not depend upon
A. Cross-section of the wire
B. Length of the wire
C. Number of free electrons
D. Magnitude of the current

Answer 1

Hint:The drift velocity is the rate of distance covered by the charge particle between two consecutive collisions from neighbouring atoms in an atom. The time taken to cover the distance between two consecutive collisions is called the relaxation time period for the charge in motion.

Formula used:
\[{v_d} = \dfrac{J}{{ne}}\]
where \[{v_d}\] is the drift velocity, \[J\] is the current density, n is the number of free electrons per unit volume and e is the charge on the electron.

Complete step by step solution:
The length of the wire used practically is generally of greater order than the interatomic distance of the material. So, when we take the distance between the consecutive collisions of the charges in a conductor then it is relatively very small as compared to the length of the wire.

Using the formula of drift velocity,
\[{v_d} = \dfrac{J}{{ne}}\]
Where, J is the current density of the wire with current I flowing across the cross-sectional area A.
\[J = \dfrac{I}{A}\]
Using conservation of charge, the rate of flow of charge in a conductor with constant potential across the length is equal throughout the length of the conductor.

Depending on the cross-section of the wire, the current density changes and so does the drift velocity. $n$ is the number of free charges per unit volume. It depends on the material and its atomic structure. So the drift velocity depends on the number of free electrons per unit volume.

When we change electric current then the current density changes and so the drift velocity. So, the drift velocity depends on the cross-section of the wire (A), the number of free electrons per unit volume (n) and the magnitude of the electric current. Hence, it doesn’t depend on the length of the wire.

Therefore, the correct option is B.

Note: Larger is the resistance of the material, the electron will have more opposition to move throughout the material and hence the drift velocity will be less.