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What is meant by an "inclined magnetic field"? How is it different from the usual magnetic field?

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An inclined magnetic field is just a magnetic field with a nonzero inclination. Inclination is the angle between the direction of the vector $\vec B$ and another, preferred direction in the problem. In astrophysics, they usually mean the radial direction. By the radial direction, I mean the normal (perpendicular) direction to the surface (of the Sun etc.).

So non-inclined magnetic field is radial; an inclined magnetic field has field lines that are twisted around the Sun (or another object) a little bit. To summarize, the adjective "inclined" doesn't carry any special physical content - it just refers to the geometrical arrangement of the objects relatively to the field.

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There is no special significance attached to the term.

Without seeing the context we can't know for certain, but "inclined" almost must refer to the orientation of the field (with respect to what will depend on the problem, but quite possible the horizontal or vertical axis of the system).

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+1 My favorite example is MRI where an inclined field with an intensity gradient is used. Since the resonant frequency of the protons depends on field intensity, that is effectively used to scan a slice through the volume. (I need to re-read how that works.) – Mike Dunlavey Nov 29 '11 at 2:39

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