- #1
Mumba
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Find the fi rst integrals of motion for a particle of mass m and charge q in a magnetic field given by the vector potential (scalar potential [tex]\Phi[/tex]= 0)
(i) of a constant magnetic dipole [tex]m_{d}[/tex]
[tex]A=\frac{\mu_{0}}{4 pi}\frac{m_{d} \times r}{r^{3}}[/tex]
Hint: Cylindrical coordinates are useful.
I think what i should do is to compute A for cylindrical coordinate system and then use Lagrangian mechanics to get a equation of motion? Is this correct? (we have the charge q given, so we can use the kinetic engergy?)
I tried to compute A but i don't really understand what to do with the magnetic dipole (as a vector)? Whats the story whith that scalar potential?
Thanks for your help,
Mumba
(i) of a constant magnetic dipole [tex]m_{d}[/tex]
[tex]A=\frac{\mu_{0}}{4 pi}\frac{m_{d} \times r}{r^{3}}[/tex]
Hint: Cylindrical coordinates are useful.
I think what i should do is to compute A for cylindrical coordinate system and then use Lagrangian mechanics to get a equation of motion? Is this correct? (we have the charge q given, so we can use the kinetic engergy?)
I tried to compute A but i don't really understand what to do with the magnetic dipole (as a vector)? Whats the story whith that scalar potential?
Thanks for your help,
Mumba