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## Main Question or Discussion Point

Hey all, I'm having some issues with electromagnetism here.

Let's say we have a particle with magnetic moment ##\vec{\mu} = \mu_0 \hat{x}## and magnetic field ##\vec{B(x)} = B_0 \frac{x}{a} \hat{x}## where ##\mu_0,B_0,a## are constants.

If we assume that the magnetic field ##B_0## is far, far bigger than the magnetic field produced by the dipole moment itself, we can assume that the potential ##U(x) =- \vec{\mu} \cdot \vec{B(x)}## has a corresponding conservative force field ##\vec{F} =- \nabla U(x) = \nabla ( \vec{\mu}\cdot \vec{B(x)}) = \mu_0 B_0 \frac{1}{a} \hat{x}##...

Which means that this dipole will drift along ##\hat{x} ##! How is this possible? The magnetic force can only be perpendicular to the current from the magnetic moment, it can never point in the same direction as the magnetic field that creates it!

Let's say we have a particle with magnetic moment ##\vec{\mu} = \mu_0 \hat{x}## and magnetic field ##\vec{B(x)} = B_0 \frac{x}{a} \hat{x}## where ##\mu_0,B_0,a## are constants.

If we assume that the magnetic field ##B_0## is far, far bigger than the magnetic field produced by the dipole moment itself, we can assume that the potential ##U(x) =- \vec{\mu} \cdot \vec{B(x)}## has a corresponding conservative force field ##\vec{F} =- \nabla U(x) = \nabla ( \vec{\mu}\cdot \vec{B(x)}) = \mu_0 B_0 \frac{1}{a} \hat{x}##...

Which means that this dipole will drift along ##\hat{x} ##! How is this possible? The magnetic force can only be perpendicular to the current from the magnetic moment, it can never point in the same direction as the magnetic field that creates it!