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the force on a magnetic moment z in a nonuniform magnetic field bz is given by if a beam of silver atoms travels a horizontal distance of 1 m through such a field and each atom has a speed of 100 m/s, how strong must the field gradient dbz /dz be in order to deflect the beam 1 mm?

2 Answers

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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.

User Thilak Raj
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3 votes

Final answer:

The field gradient dBz/dz must be 1.6 x 10^14 T/m.

Step-by-step explanation:

The force on a magnetic moment z in a nonuniform magnetic field Bz is given by the equation Fz = μBz dBz/dz, where μ is the magnetic moment. To find the field gradient required to deflect the beam by 1 mm, we can use the formula Fz = qv dBz/dz and solve for dBz/dz.

Given that the beam of silver atoms travels a horizontal distance of 1 m and each atom has a speed of 100 m/s, we can substitute the values and solve for dBz/dz:

Fz = qv dBz/dz

1 mm = (1 m)(1.6 x 10^-19 C)(100 m/s) dBz/dz

Solving for dBz/dz, we find that it must be 1.6 x 10^14 T/m in order to deflect the beam by 1 mm.

User Matin Sasan
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8.4k points