# Is the magnetic field zero inside an ideal conductor carrying a current?

By an ideal conductor, I mean one with zero resistance.

The question is not about a superconductor. As I know superconductor and conductor with zero resistance are not the same thing. The question is more about what happens to magnetic field inside a wire when its resistance approaches null.

• Possible duplicate of Perfect conductor and magnetic field Jul 27, 2016 at 15:30
• It is a follow up to Is the electric field zero inside an ideal conductor carrying a current? Jul 27, 2016 at 15:53
• @ACuriousMind The question is not a duplicate of this one. That question is about whether external magnetic field can penetrate inside superconductors. While this question is about magnetic field induced inside ideal conductor by current flowing through it. Imho, different questions. Please, unmark as duplicate if agree. Jul 31, 2016 at 16:00
• Recommend for reopening. As mentioned, the marked duplicate is about superconductors, while this is not. May 10, 2018 at 20:24

In general, it is not.

Assume a constant current flowing through a cylindrical conductor.

Applying Ampere's circuital law for a surface inside the cylinder:

$$\oint {\vec Bd\vec l = {\mu _0}\int\!\!\!\int {\vec J} d\vec s}$$ $$B2\pi r = {\mu _0}J{{\pi {r^2}} \over {\pi {a^2}}}$$ $$B = {{{\mu _0}} \over {2\pi {a^2}}}Jr$$

According to Wikipedia

In perfect conductors, the interior magnetic field must remain fixed but can have a zero or nonzero value.

Require a constant magnetic flux - the magnetic flux within the perfect conductor must be constant with time. Any external field applied to a perfect conductor will have no effect on its internal field configuration.

According to this site

The interior magnetic field is zero while the surface magnetic field is perpendicular to both the current density and the surface normal.