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Consider a cube of metalic material (either it is paramagnetic or diamagnetic can be both discussed). An external magnetic field $\textbf{B}$ is applied along the +x axis.

We expect $\textbf{B}$ to be affected by the material. There are several ways to explain such mechanism. One of them is to consider every atom as having a small loop of current $I$, creating a magnetic moment $\textbf{m}=I \textbf{S}$. When an external magnetic field is applied, these magnetic moments will line up, making the magnetic field stronger.

Another perspective is related to magnetic charges, or, monopoles. When an external magnetic field $\textbf{B}$ is applied, these charges behave like electric charges in an electric field. Hence, they have a polarizing effect. "Positive" (North) charges will accumulate at the +x side and "negative" ones will be at the -x side of the material. By creating an induced magnetic field $\textbf{B'}$ in the opposite direction of $\textbf{B}$, this will weaken the magnetic field.

The above two statements seems contradicting. Which one is right?

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3 Answers 3

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Magnetic monopoles do not exist and therefore that particular argument is never going to work.

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Your first paragraph is wrong. Because of Lenz's law, applying a magnetic field to a current loop reduces the magnetic field. This is called a diamagnetic material with $\mu<1$. The second paragraph is wrong because, as the first answer says, there are no magnetic poles. In paramagnetic and ferromagnetic materials, the atoms have permanent magnetic moments due to the intrinsic spin magnetic moments of electrons. These magnetic moments line up with the magnetic field, so that $\mu>1$.

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  • $\begingroup$ So to summarize, the answer depends on whether the material is diamagnetic, paramagnetic or ferromagentic, right? If it is the former one then the magnetic field is decreased, while for the latter two $\textbf{B}$ will increase. $\endgroup$
    – Cyh1368
    Commented Jun 10, 2023 at 6:20
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In fact, neither "picture" is right, they are pictures so that you can visualize a model of reality. There is a microscopic "vacuum" field between the atoms, and also between the electron and the nucleus. This microscopic, or rather femto/pico/nano-scopic field is both temporally and spatially strongly inhomogeneous and fluctuating, and there are two ways that its macroscopic average manifests itself. It is partly and mostly a bulk effect and partly and mostly a superficial surface effect. In macroscopic physics and engineering neither is more fundamental than the other. In the old days physicists and still today most engineers have preferred to think of fictitious charges as the source of magnetization because it is easier to visualize it; modern views are more leaning to view sources as being from currents but both macroscopic source concepts are fictitious mathematical constructs. Both can be traced to the so-called Helmholtz decomposition theorem, see posts, and, and.

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  • $\begingroup$ So in reality, which picture describes the correct phenomenon? $\endgroup$
    – Cyh1368
    Commented Jun 6, 2023 at 23:11
  • $\begingroup$ In general, you need both, but there are special cases when the geometry allows you to infer one immediately or easier than the other. One such example is a toroid with a high permeability and a wire wound around it. The current gets you the $H$ field but you need the $B$ and its flux to calculate any induced voltage. A small gap in the yoke will let you get the B first and from that the H. The same problem shows up in E v. D. Macroscopic physics and engineering need both fields. $\endgroup$
    – hyportnex
    Commented Jun 7, 2023 at 0:54

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