The Lagranian of a relativistic charged particle of mass m, change e and velocity moving in an electromagnetic field with vector potential A is e =-me² √√1-B²+ A .The field of a dipole of C magnetic moment along the polar axis is usin described by the vector potential A = where is the polar angle and is the azimuthal angle. The corresponding Hamiltonian H = ymc². Now consider a gauge transformation A'=A+Vx (r,0,0) where x is an arbitrary function. Then the transformed Hamiltonian is given by 1. ymc² + ²√x.v C 3. mc² Y ea 2y mê 4. ymc² - ²x.v C
The Lagranian of a relativistic charged particle of mass m, change e and velocity moving in an electromagnetic field with vector potential A is e =-me² √√1-B²+ A .The field of a dipole of C magnetic moment along the polar axis is usin described by the vector potential A = where is the polar angle and is the azimuthal angle. The corresponding Hamiltonian H = ymc². Now consider a gauge transformation A'=A+Vx (r,0,0) where x is an arbitrary function. Then the transformed Hamiltonian is given by 1. ymc² + ²√x.v C 3. mc² Y ea 2y mê 4. ymc² - ²x.v C
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Transcribed Image Text:The Lagranian of a relativistic charged particle of
mass m, change e and velocity moving in an
electromagnetic field with vector potential A is
L=-mc² √√1-B²+ A .The field of a dipole of
magnetic moment along the polar axis is
described by the vector potential À= μsin
where is the polar angle and is the azimuthal
angle. The corresponding Hamiltonian H = ymc².
Now consider a gauge transformation
A'=A+Vx (r,0,0) where x is an arbitrary
function. Then the transformed Hamiltonian is
given by
1. ymc² + ²√x.v
C
3.
mc²
Y
2 y mê
4. ymc²-√x.v
C
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