Section 5.1 – Magnetic Fields
* the magnetic force was known in antiquity, but was more difficult to quantify
~ no magnetic (point) charge (monopole); 1-d currents instead of 0-d charges
~ static electricity was produced in the lab long before steady currents
~ predominant effect in nature involves magnetization, not electric currents
* for magnetism it is must more natural to start with the concept of field
~ compass points N
because it aligns with
the Earth’s magnetic field
~ iron filings chain up to
show physical “field lines”
~ bar magnet field
lines resemble an
electric dipole
* what is the main difference?
~ two interconnected differences related to “flux” and “flow”
~ the difference between “internal” and “external” dipole
~ lines of flux conserved
~ flow is rotational
~ sources/sinks of flux
~ conservative flow (potential)
~ this is responsible for difference between E and B field equations
and difference between dielecrics and permanent magnets
* no magnetic monopole!
~ N/S poles cannot be separated
~ reason: magnetic dipoles are actually current loops
~ note: field lines are perpendicuar to source current
* discovery by Hans Christian Oersted (1820)
~ current produces a magnetic field
~ generalized to the force between wires by Ampere, Biot and Savart
* Ampere
~ definition of Ampere [A]
~ definition of Tesla [T]
and Gauss (CGS units)
for two wires separated by distance d
Coulomb [c]
Section 5.2 – Current Elements; Lorentz Force Law
* magnetic force law
~ the combination
occurs frequently, it is called the “current element”
~ units: A m = C m/s ~ qv, much like a “charge element”
* current density
* conservation of charge: Kirchov’s current law
* relation between charge and current elements
~ written as 4-vectors
* Lorentz force law
* Magnetic forces do no work
tangential acceleration (not quite)
radial acceleration
(always)
“gas pedal”
“steering wheel”
~ similar to the normal force which only deflects objects