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We know there is an energy associated with magnetic fields is $$\frac{1}{2}\mu B^2$$ Consider a magnetic field perpendicular to a conductor (any metal). Shouldn't it theoretically be possible to make magnetic field inside the metal $0$ (similar to the way the electric field inside a metal is $0$ by redistributing charges) by creating circular current loops in the metal do oppose the magnetic field? This would minimize energy inside the metal right? Why does this not actually happen?

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  • $\begingroup$ It actually happens in superconductors. $\endgroup$ – flaudemus Mar 28 at 7:33
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Relevant answer: Energy inside a material is given by summing all the contributions by each dipole moment whose energy is given by $E= -\vec{m}\cdot\vec{B}$

So 0 is not the lowest energy. And the least energy is when $m$ and $B$ align.

Clarification: The main reason is that magnetic monopoles don’t exist (that we know of). But electric monopoles exist and they are point charges. The cancellation of the external field comes due to the movement of these charges. In that sense we can’t have a 0 magnetic field analogous to the electric field. However there are other mechanisms by which we get a 0 magnetic field.

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  • $\begingroup$ The field inside a diamagnetic material is 0. This is false. Maybe you're thinking of Meissner effect, occurring in superconductors. In a diamagnetic substance, with proper geometry, magnetic field can be slightly less than outside, but never zero. $\endgroup$ – Elio Fabri Mar 30 at 20:00
  • $\begingroup$ Thank you. I was mistaken. I have removed the statement. $\endgroup$ – user3518839 Mar 30 at 20:56

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