Question

For the conductor shown in figure alongside

A) $V_{d_A} = V_{d_B}$
B) $V_{d_A} > V_{d_B}$
C) $V_{d_A} < V_{d_B}$
D) $\text{The drift speed varies randomly}$

Answer 1

In physics, a drift velocity is the average velocity attained by charged particles, such as electrons, in a material due to an electric field. In general, an electron in a conductor will propagate randomly at the Fermi velocity, resulting in an average velocity of zero.
Mathematically we can say that:
$I = neA{v_d} \\\ {v_d} = \dfrac{I}{{neA}}$
where ${v_d}$ is drift velocity of electrons
Other symbols have usual meanings.

Complete step by step solution:
As we know that current is flowing in the conductor due to movement of the electrons in the particular direction.so if we apply a potential difference across the conductor then we get some current in the wire.
Let us assume a uniform current flows in the conductor because the numbers of electrons passing through a unit area is equal.
The current in the conductor is calculated by the formula
$I = neA{v_d}$
Where, I = current in the wire
A = cross sectional area of the wire
n =number of electrons in the wire
${v_d}$ = drift velocity of the wire
e = value of charge on the electron
Now ${v_d} = \dfrac{I}{{neA}}$
$\therefore \dfrac{I}{A} = J$
where J is current density of the wire
As we all know that current density is constant in the wire
$\Rightarrow {v_d} = \dfrac{J}{{ne}}$
finally, we conclude that
$\Rightarrow V_{d_A} = V_{d_B}$
So drift velocity will only depend upon on the number of electron on the wire
Hence we can say that drift velocity does not depend on the cross sectional area of the wire.

Correct answer will be option A.

Note: Current density of a wire is defined as the ratio of current and cross sectional area. We all know that the current density of a conductor is always constant because it is the ratio of current and area.
Mathematically $J = \dfrac{i}{A}$