Rocky Raccoon
Jan31-11, 08:30 AM
1. The problem statement, all variables and given/known data
Find rho(r,t) and j(r,t) for the following:
a) point charge q in uniform motion
b) electric dipole p in uniform motion
c) magnetic dipole m in uniform motion
2. Relevant equations
j(r,t) = v rho(r,t), so if we know rho, we know j
3. The attempt at a solution
a) is trivial - rho(r,t) = q delta (r - vt), where delta is Dirac's delta and v is the velocity of the charge
b) is also easy - rho(r,t) = - p . grad (delta(r - vt))
c) is where I don't know how to proceed.
I wish to solve the wave equation for the potentials A and phi but don't know what are the sources rho and j in the case of a magnetic dipole moment m.
Find rho(r,t) and j(r,t) for the following:
a) point charge q in uniform motion
b) electric dipole p in uniform motion
c) magnetic dipole m in uniform motion
2. Relevant equations
j(r,t) = v rho(r,t), so if we know rho, we know j
3. The attempt at a solution
a) is trivial - rho(r,t) = q delta (r - vt), where delta is Dirac's delta and v is the velocity of the charge
b) is also easy - rho(r,t) = - p . grad (delta(r - vt))
c) is where I don't know how to proceed.
I wish to solve the wave equation for the potentials A and phi but don't know what are the sources rho and j in the case of a magnetic dipole moment m.