Final answer:
The force on a magnetic moment in a nonuniform magnetic field is given by F = ∂(Bz)/∂z. To deflect the beam by 1 mm over a distance of 1 m, we can use the formula F = ma and rearrange it to solve for the magnetic field gradient ∂(Bz)/∂z. By calculating the acceleration using the given information and using the formula a = v^2/d, we can determine the magnetic field gradient required.
Step-by-step explanation:
The force on a magnetic moment z in a nonuniform magnetic field Bz is given by:
F = ∂(Bz)/ ∂z
In order to deflect the beam by 1 mm over a distance of 1 m, we can use the formula for force:
F = ma
where m is the mass of an atom and a is the acceleration. We can rearrange the formula to solve for the magnetic field gradient:
∂Bz)/∂z = F/m
Given that the speed of the atoms is 100 m/s, we can use this information to calculate the acceleration. Assuming the mass of a silver atom is 108 atomic mass units, we can convert it to kilograms and use the formula:
a = v2/d
where v is the velocity and d is the distance traveled. Plugging in the values, we can solve for acceleration and then calculate the magnetic field gradient.