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## Homework Statement

the force on a magnetic moment with z component u(z) moving in an inhomogenous magnetic field is given by Equation 7-51: F(z)=u(z)*(dB/dz). If the silver atoms in the stern gerlach experiment traveled horizontally 1 meter through the magnet and 1 meter in a field free region at a speed of 250 meters/second, what must have been the gradient of B(z) , dB(z)/dz, in order that the beams each be deflected a maximum of .5mm from the central , or no field, position?

## Homework Equations

F(z)=u(z)(dB/dz)

u(z)=-m(Ag)*u(B)

u(B)=9.27e-24 Joules/tesla

v=250m/s

x=1 meter

distance in field free region=1m

U=u(z)*B

## The Attempt at a Solution

F(z)=u(z)*(dB/dz)=> m(Ag)*gravity=-m(Ag)*u(B)*dB/dz.

masses cancel , so I'm left with::

gravity=-u(B)*dB/dz

-gravity/u(B)=dB/dz

to find B(z), I apply the equation U=u(z)*B. U=mgh and I alrealdy know what u(z) is equal to from the first part of the problem. THEREFORE, mgh/u(z)=B(z) . I don't know what relevancy the velocity and the deflected maximum distance served in finding B(z) and dB(z)/dz