Diamagnets have the property that they "dampen" the effects of an external magnetic field by creating an opposing magnetic field. The diamagnet thus has an induced dipole moment that is anti- aligned, such that the induced north pole is closer to the north pole creating the external field. An application of this is that diamagnets can be levitated e. Now, the mathematics of generally describing a force by a non-uniform field on a dipole is a little beyond the scope of this course, but we can still work through an approximation based on energy. Essentially, whenever the theoretical loss of gravitational potential energy from "falling" no longer can "pay the cost" of increasing the magnetic potential energy, the object no longer wants to fall.

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Chapter1: Units, Trigonometry. And Vectors
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Diamagnets have the property that they "dampen" the effects of an external magnetic field by
creating an opposing magnetic field. The diamagnet thus has an induced dipole moment that is anti-
aligned, such that the induced north pole is closer to the north pole creating the external field. An
application of this is that diamagnets can be levitated 2.
Now, the mathematics of generally describing a force by a non-uniform field on a dipole is a little
beyond the scope of this course, but we can still work through an approximation based on energy.
Essentially, whenever the theoretical loss of gravitational potential energy from "falling" no longer
can "pay the cost" of increasing the magnetic potential energy, the object no longer wants to fall.
Suppose a diamagnetic object floats above the levitator where the magnitude of the magnetic field
is 12 T, which is inducing" a magnetic dipole moment of 4.6 LA - m² in the object. The magnetic
field 1.9 mm below the object is stronger with a magnitude of 33 T. What is the approximate mass
of the floating object?
Give your answer in units of g (i.e., x10-3 kg), and use g = 9.81 m/s?. You may assume the object's
size is negligible.
Transcribed Image Text:Diamagnets have the property that they "dampen" the effects of an external magnetic field by creating an opposing magnetic field. The diamagnet thus has an induced dipole moment that is anti- aligned, such that the induced north pole is closer to the north pole creating the external field. An application of this is that diamagnets can be levitated 2. Now, the mathematics of generally describing a force by a non-uniform field on a dipole is a little beyond the scope of this course, but we can still work through an approximation based on energy. Essentially, whenever the theoretical loss of gravitational potential energy from "falling" no longer can "pay the cost" of increasing the magnetic potential energy, the object no longer wants to fall. Suppose a diamagnetic object floats above the levitator where the magnitude of the magnetic field is 12 T, which is inducing" a magnetic dipole moment of 4.6 LA - m² in the object. The magnetic field 1.9 mm below the object is stronger with a magnitude of 33 T. What is the approximate mass of the floating object? Give your answer in units of g (i.e., x10-3 kg), and use g = 9.81 m/s?. You may assume the object's size is negligible.
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