I found on this site a formula (4.101). It describes wich force acts on matter in an inhomogeneous magnetic field. $ F_z = m_z * \frac{\partial B_z (z0)}{\partial z}$ What does the fraction consist of? What does the $z$ mean?
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What you call "the fraction" is the derivative of the magnetic induction in respect position along the z axis. This is the factor that measures the inhomogeneity of the magnetic field. It is actually the component of the gradient of the magnetic field along the z axis. z is an index for one of the direction or axes in a Cartesian coordinate system. The other two directions are usually labeled x and y. So the formula shows how the component of the magnetic force along the z axis is related to the magnetic moment along the same axis and the gradient of the magnetic field (again, along same axis).
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$\begingroup$ so does the $z0$ in $\partial B_z(z0)$ mean that we just look at the change of the magnetic field in the z direction? $\endgroup$– Max KCommented Aug 13, 2016 at 15:21
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$\begingroup$ No, the zo indicates that you calculate the partial derivative at z=zo. $\endgroup$– nasuCommented Aug 13, 2016 at 17:49