Gauss’ Law for magnetic fields There are no magnetic “charges”.

Gauss’ Law for magnetic fields

Ampere’s Law

Is there a current passing through the inside of this path?

Ampere’s Law is a relationship between: the magnetic field around a closed path, and the net current passing through an open surface bounded by the path.

For a very long wire (L >> R):

Ampere’s Law

Ampere’s Law does not depend on the size and shape of the closed path, or of the surface bound by the path. It also does not depend on the position of the current inside the path. Like Gauss’ Law, we can use it to find the field in some situations with a high level of symmetry.

Magnetic field inside a cylindrical current-carrying conductor “Amperian loop”

Magnetic field inside a cylindrical current-carrying conductor “Amperian loop” (direction from right-hand rule!)

Magnetic field outside a cylindrical current-carrying conductor

Magnetic field inside a solenoid

n loops per unit length

Magnetic field inside a solenoid n loops per unit length

Maxwell’s Equations (so far…) *Not complete