# Are poles on the inside diameter of a hollow diametrically magnetized sphere reverse that on the outside?

On the inside diameter of a hollow, diametrically magnetized sphere like in the image below, are the poles reverse that of the outside, or, are the poles on the inside the same as on the outside? For example, if a smaller sphere is placed within this sphere, would it orient its poles in the same direction as this sphere (the pole on the inside of the sphere is reverse), or, would it orient its poles in the opposite direction (the poles on the inside of the sphere are same as on outside)?

• The point is I was given contradictory answers on what the magnetic field looks like on the inside of a hollow sphere, specifically. Roughly 50% have said that there are opposite poles on the inside and outside diameter of the sphere, and another 50% have said that the sphere has a whole is diametrically magnetized, the same pole on the inside and outside diameter of the sphere. – user612 May 10 at 0:46
• Based on the idea of scientific consensus, it seems like there should be a single opinion that people converge on. Having talked with people who are engineers, physicists and so on, they give two separate opinions. – user612 May 10 at 0:47
• edited the question to ask exactly that instead – user612 May 10 at 0:54

The problem you are running into is one of terminology, not physics. There are actually two different quantities that go by the name "magnetic field." There is the field $${\bf B}$$ that appears in the Lorentz Force Law: $${\bf F}=q({\bf E}+{\bf v}\times{\bf B})$$ (in MKS units). This field $${\bf B}$$ is also the one that appears in Faraday's Law. However, there is another quantity $${\bf H}=\frac{1}{\mu_{0}}{\bf B}-{\bf M}$$ (where $${\bf M}$$ is the magnetization–the magnetic dipole moment density inside matter) that is also frequently known as the "magnetic field."
The reason for the confusing terminology is that while $${\bf B}$$ is the more fundamental field, $${\bf H}$$ is easier to calculate when there are magnetic materials present, because $${\bf H}$$ depends directly on the free current, which is what you control with a battery. $${\bf H}$$ also behaves more like the electric field $${\bf E}$$ than $${\bf B}$$ does; in particular, in the absence of free currents, both $${\bf E}$$ and $${\bf H}$$ have vanishing curl. So it was thought, in the nineteenth century, that $${\bf H}$$ was the more fundamental field, and $${\bf B}$$ was known as the "magnetic induction" or "magnetic flux density." Nowadays, while everyone recognizes that $${\bf B}$$ is the basic field, and $${\bf H}$$ is a convenient auxiliary quantity, there is still no agreement on which quantity should be called "magnetic field."
In vacuum, the difference between the $${\bf B}$$ and $${\bf H}$$ is unimportant; they just differ by a constant factor. However, when magnetic materials are present, they two quantities can behave quite differently. The north and south poles of a permanent magnet act like sources of $${\bf H}$$, with the lines of $${\bf H}$$ emerging from the N pole and ending at the S pole. On the other hand, the lines of $${\bf B}$$ (which is always divergenceless) form closed loops; this means that they point in opposite directions inside and outside a permanent magnet, since they much loop back around to where they started.
Here is an image of what $${\bf H}$$, $${\bf B}$$, and $${\bf M}$$ are all doing inside a uniformly magnetized block of material.