The magnetic field due to a wire in 3D

1. The magnetic field due to a wire in 3D Like Coulomb’s Law: (For an infinite line charge)

2. Let’s think back to electrostatics As far as we know, there is no magnetic equivalent of charge. Therefore, magnetic field lines never begin or end. Consequently, Gauss’ law of no use in magnetostatics, since there is nothing with which to equate the flux of B. By the way..... .... we just derived (wrote down) the 2nd Maxwell equation! • This is Gauss’ law, i.e. the more fundamental Maxwell equation. • It tells us that E-fields begin and end on electric charges. • Provides a simple method for calculating E for certain symmetries.

3. Recall: electrostatic forces are conservative • This allowed us to define a scalar potential V. • Also implies.. • Consequently, this integral is not much use in electrostatics. • It is very important in electrodynamics (Maxwell’s 4th equation). • However, this is because its not equal to zero in electrodynamics.

4. Maxwell’s 3rd equation (a.k.a. Ampère’s Law) Right- hand- rule

5. The Magnetic Field of a Dipole (P. 26-1) Electric dipole Magnetic dipole Bar magnet At large distances (z >> R) along the z-axis