Question

A steady electric current is flowing through a cylindrical conductor:
(This question has multiple correct options)
(A) The electric field at the axis of the conductor is zero.
(B) The magnetic field at the axis of the conductor is zero.
(C) The electric field in the vicinity of the conductor is zero.
(D) The magnetic field in the vicinity of the conductor is zero.

Answer 1

Hint To solve the question, you first need to know that if the electric field inside is zero, the flow of current would not be possible given that there would be no pull on the electrons. Also, to find the correct option for the magnetic field, you need to use the Biot-Savart Law to check where the magnetic field would be zero and why.

Complete step by step answer:
As told in the hint section of the solution to the asked question, for any current to flow inside a conductor, there must always be a presence of electric field so that the electrons experience a force or pull and thus carry the current across the conductor. If there is no electric field at the axis of the conductor, as said in the option (A), then there would be no flow of current in the cylindrical conductor, let alone the flow of a steady current.
So, we can confidently say that option (A) is a wrong option.
As for the magnetic field at the axis of the cylindrical conductor, using the Biot-Savart law, we can see that the magnetic field at the axis of a cylindrical conductor carrying a steady current will be nothing but zero since at the axis, the radius of the circular cross-sectional area is zero, there would be no amperical cross-section to consider inside which a current flows. So, the option (B) is correct as the magnetic field at the axis of the conductor is zero.
So, we can safely say that the option (B) is a correct statement and thus, a correct option.
Since the net charge through any possible cross section of the cylindrical conductor carrying the steady current is zero as it has the equal number of electrons and protons to balance the charge content of the conductor, the electric field in the vicinity of the conductor is nothing but zero. Hence, we can confidently say that the option (C) is a correct option.
As for the magnetic field in the vicinity of the conductor, it will not be zero, which is very obvious from the Biot-Savart law. It is also visible that any cross section considering the point in the vicinity of the conductor has a steady current flowing inside it, thus, making the magnetic field at the point a non-zero quantity.
So, option (D) is wrong.

Hence, the correct answer is options (B) and option (C).

Note Many students will tick the first option as the correct one considering that the value of radius at the axis is nothing but zero without even giving a thought about the fact that if the electric field at the axis would be zero, there would be no current flowing through the conductor either, hence, losing the marks.