23. ročník, úloha II . P telekinesis !!! chybí statistiky

Fyzikální korespondenční seminář UK MFF
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23 . II . P
23. ročník, úloha II . P . . . telekinesis !!! chybí statistiky !!!
Where does a permanent magnet take the power to lift stuff? We know that the magnetic
force does no work. Lorenz equation, F = q(v × B), says that the magnetic force is perpenœ
dicular to the velocity of a moving charge and therefore only changes its direction.
In fact, the formula for the magnetic force does not imply zero work. Such a conclusion
would be valid for a single charged particle without any other external forces. However, if
there are some constraint forces (for example, consider an electron bound to the surface of
a positively charged body by the electrostatic force) the magnetic force can act against those
forces, pushing the particle to a configuration with a higher potential energy. If this is the case,
the magnetic force must perform some work.
It is also noteworthy that the magnetic field must be inhomogeneous to attract a magnetized
body. (Any magnetic field created by a magnetic dipole is always inhomogeneous except for
the centre of a dipole.) The total force of the magnetic force acting on a magnetic dipole is
given by the following formula
F = grad(m · B)
where m denotes magnetic dipole moment. In case of a small loop, we have m = IS where I
stands for the electric current in the loop and S is the area of the loop (oriented to its normal).
A homogeneous magnetic field would only cause Larmor precession of a body but the total
force would be zero.
Marek Nečada
[email protected]
Fyzikální korespondenční seminář je organizován studenty UK MFF. Je zastřešen Oddělením
pro vnější vztahy a propagaci UK MFF a podporován Ústavem teoretické fyziky
UK MFF, jeho zaměstnanci a Jednotou českých matematiků a fyziků.
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