Question

A steady current is set up in a metallic wire of non-uniform cross-section. How will the rate of flow of electrons $\left( R \right)$ be related to the area of cross-section of the wire?

Answer 1

The rate of flow of charges through a wire is known as current. The current is not dependent on the dimensions of the wire. Current density is the current flowing through the unit area of the cross section. Hope these all may help you to solve this question.

Complete step by step answer:
A supply of electric charges or electrons which can flow freely, creates a kind of push to move the charges through the circuit and develops a path for the movement of the charges. Electrons are not moving along the wire such as the cars moving on a road. As we all know, any material through which electricity can pass is made of atoms. Each atom contains electrons in it. If we add new electrons in a conductor, they will get joined with the atoms, and each atom will be delivering an electron to the next atom. This way energy is being transferred in a conductor. The equation of current in accordance to ohm’s law can be written as,
$I=\dfrac{V}{R}$
Where $V$ be the potential of the wire and $R$ be the resistance of the wire.
From this we can say that the current is not dependent on the dimensions of a conductor such as the length, area of cross section and so on. Therefore even the area of the wire is altered, the current through the wire will remain constant. Only the current density, electric field and electric potential are inversely proportional to the area of the conductor.
$\begin{aligned} & J\propto \dfrac{1}{A} \\\ & E\propto \dfrac{1}{A} \\\ & V\propto \dfrac{1}{A} \\\ \end{aligned}$
Hence the question has been answered.

Note:
Specifically the electric current is the flow of electric charge. In electric circuits this charge is sometimes taken by moving electrons in a circuit. Electrons and protons are the elementary substances that constitute electric current flowing through the wires which are made up of metals. When the electrons are forced to get out of their orbits, it can cause a lack of electrons. These electrons will continuously move in a wire referred to as Electric Current. In the case of solid conductors, the electric current will be directional from negative-to-positive as electrons from one atom to the next atom.