Please show work and explain thought process. If you have any questions please a

Question

Please show work and explain thought process. If you have any questions please ask.

Consider a particle of charge q and mass m in the vicinity of an object (such as the Earth) with a magnetic field. The field is described in spherical coordinates by a magnetic vector potential in the azimuthal direction, A = A phi (r, theta ) phi ,and is axisyminetric. The magnetic vector potential Is chosen to go to zero at r rightarrow infinity . Only the force from the magnetic field acts on the particle. Express the z-component of the particle's angular momentum in terms of its coordinates (r, theta , phi ) and the components of its velocity (vr, v theta , v phi). Express the z component of torque on the particle in terms of its position, velocity, and the magnetic vector potential and its derivatives.

Explanation / Answer

Hi,

Please find the link to the answer. And let me know if anything is unclear.

Part (a)

https://drive.google.com/file/d/0BzsApW5yffhsUVhfQldfOEY4Sms/edit?usp=sharing
https://drive.google.com/file/d/0BzsApW5yffhsd1VJbjBKYUl5R00/edit?usp=sharing

Part(b)

https://drive.google.com/file/d/0BzsApW5yffhsaWJhUlZnQ0g3SmM/edit?usp=sharing

https://drive.google.com/file/d/0BzsApW5yffhsLU1McUU5WVBSS0k/edit?usp=sharing

Cheers,

Saurav

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