Question

A steady electric current is flowing through a cylindrical conductor
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
Here we are going to discuss the property of conductors, i.e. charge inside the conductor is always zero. So the electric field inside the conductor is also zero. And the properties of magnetic field in the axis, i.e axis inside the conductor have always zero magnetic field and axis outside of conductor is always constant but not zero.

Complete Step by Step Solution
Let us take a solid cylindrical conductor have an axis “l” where “$l_1$“is outside of the conductor and “$l_2$“is inside of the conductor and “$l_3$“is outside of the conductor,
(as shown in figure)

Now, the axis has three part i.e $l_1$, $l_2$ and $l_3$
So, $l_1$ and $l_3$ is present outside of the conductor therefore the axis of solid cylindrical conductor has zero electric field only at $l_2$ part not at $l_1$ and $l_3$ .Therefore, we concluded that
“The electric field at the axis of the conductor is not zero.”
Also,we concluded that
“The magnetic field at the axis of the conductor is always zero.” (property of magnetic field)
Now, charge in the vicinity of the conductor is zero so the electric field will also be zero.
Therefore we concluded that-
“the electric field in the vicinity of the conductor is zero”.
Now, the magnetic field in the vicinity of the conductor is always constant but not zero
Therefore we concluded that,
“The magnetic field in the vicinity of the conductor is not zero.”
Option (C) is correct.

Note
Properties of a conductor in electrostatic equilibrium; Inside a solid conductor the electric field is always zero because the charge inside the conductor is zero and the magnetic field inside a conductor is constant but not zero due to magnetic flux.