Question

A steady current is passing through a linear conductor of non-uniform cross-section. The net quantity of charge crossing any cross section per second is:
A) Independent of the area of cross-section.
B) Directly proportional to the length of the conductor.
C) Directly proportional to the area of cross-section.
D) Inversely proportional to the length of the conductor.

Answer 1

Charge is defined as the property through which the particle experiences force if it is left under the influence of the magnetic or electric field. The charge passing through any cross-section is known as current.

Complete step by step answer:

It is given in the problem that a steady current is passing through a linear conductor of non-uniform cross-section. We need to select the correct option in the problem.

Let us consider each option and find which option is correct.

Option A
The charge crossing any cross section is independent of the area of the cross section.
The charge crossing any cross section per second is defined as the current. The current is steady which means that the current is uniform throughout the cross-section; therefore the net charge crossing the cross section per second is independent to the length of the cross-section.

Let us consider option B,
Directly proportional to the length of the conductor.
The above option says that the net quantity of charge crossing any cross section per second is directly proportional to the length of the conductor.
The rate of change of charge with respect to the time is called current and it is not proportional to the length of the conductor therefore this option is not the correct answer for this problem.

Let us consider option C,
Directly proportional to the area of cross section.
The rate of change of charge is equal to current and it is independent of the area of cross section. Therefore this is not the correct option for this problem.

Let us consider the option D,
The rate of change of charge for any material is equal to the current and it does not change with length or the cross section. Therefore this is not the correct option for this problem.

The correct answer for this problem is option A.

Note: The rate of change of charge with respect to the current is independent of the length and is also independent of the area of the cross section of the conductor or else the current will vary with every other material of different length and cross section which is not a very good indication for transmission of current.