Physics 1602 9

• B = curl A

• div B = 0

  • This is obvious considering that there is no magnetic charge and Gauss’s law.
  • It also matches with div curl A = 0.

• If there is a particle moving perpendicular to the magnetic field, a force in the direction of the magnetic field is generated.

• Charge conservation imposes a strong constraint on the current density, j.

  • For example, a non-looping line cannot create a magnetic field.
    • Because charge cannot continue to move without a loop.

• Intuition:

  • Curling current -> straight field
  • Straight current -> curling field
  • I have this intuition (blu3mo)
    • It’s about $\hat{\theta }$ and $\hat{r}$.

• The current I/A absorbs the dimension of the length^2 in the volume integral.

• Equipotential curves have the same shape for both A and Φ.

  • Equipotential curves have the same direction as the vector A.
  • A and B are perpendicular.

• Ampere’s Law

  • curl B = μJ
    • It makes sense dimensionally (blu3mo).
  • It is important to check how the surface conditions are derived from here.

• Is the Earth a coil because it is a rotating charge?

Two wires are approaching.

Integrating (ρ, J) gives (σ, κ).

• In SI units, there is a dimensional difference between the magnetic field and the electric field due to c.
• This is the contribution of the cross term (B_y contributes to E_x).

Just like the electric field, the perpendicular component of the B field does not change under a boost.

• There is a variant of the cross product between a vector and a boost that resembles LT.