Fields From Charge and Current Distributions
Most recent answer: 11/04/2014
- Daniyal Ahmed (age 19)
That's a very thoughtful question. Far away from the wire, the field can be calculated treating the current as flowing along a line in the middle of the wire. Close to the wire, the distribution matters. In the middle of the wire, for example, there's zero field if the current is symmetrical around that point but there is a field if the currents on each side are different.
The same principle applies to electric fields coming from charge distributions.
As you guessed, the fields can be calculated by doing integrals over all source regions of the current or charge densities multipled by the appropriate geometrical factors for how far away that is in what direction.
The fields well outside each source region can be also expressed as the sum of monople, dipole, quadrupole, etc. components. The monopole piece is zero for magnetic fields, at least for all known sources. The other pieces depend on how the charges or currents are arranged.
(published on 11/04/2014)