daniel_i_l said:
GR explains how gravity works. Is there a similar explanation for magnetism. Maxwell showed that magnetism and electricity are two sides of the same coin. And I understand that electricity is a flow of electrons. Can that help me understand magnetism?
nearly everything that Mk wrote is correct, but IMO, is not the root issue. (where does the magnetic field come from?)
Maxwell showed that magnetism and electricity are interactive. that they have something to do with each other, but it wasn't until special relativity that they were shown to be "two sides of the same coin". one can use SR to show that the magnetic field is
nothing other than the electrostatic effect, but taking into consideration time-dilation from SR. here is something i posted here long ago about it:
The classical electromagnetic effect is perfectly consistent with the lone
electrostatic effect but with special relativity taken into consideration.
The simplest hypothetical experiment would be two identical parallel
infinite lines of charge (with charge per unit length of \lambda \ )
and some non-zero mass per unit length of \rho \ separated
by some distance R \. If the lineal mass density is small enough
that gravitational forces can be neglected in comparison to the electrostatic
forces, the static non-relativistic repulsive (outward) acceleration (at the instance
of time that the lines of charge are separated by distance R \)
for each infinite parallel line of charge would be:
a = \frac{F}{m} = \frac{ \frac{1}{4 \pi \epsilon_0} \frac{2 \lambda^2}{R} }{\rho}
If the lines of charge are moving together past the observer at some
velocity, v \, the non-relativistic electrostatic force would appear to be
unchanged and that
would be the acceleration an observer traveling along
with the lines of charge would observe.
Now, if special relativity is considered, the in-motion observer's clock
would be ticking at a relative *rate* (ticks per unit time or 1/time) of \sqrt{1 - v^2/c^2}
from the point-of-view of the stationary observer because of time dilation. Since
acceleration is proportional to (1/time)
2, the at-rest observer would observe
an acceleration scaled by the square of that rate, or by {1 - v^2/c^2} \,
compared to what the moving observer sees. Then the observed outward
acceleration of the two infinite lines as viewed by the stationary observer would be:
a = \left(1 - v^2 / c^2 \right) \frac{ \frac{1}{4 \pi \epsilon_0} \frac{2 \lambda^2}{R} }{\rho}
or
a = \frac{F}{m} = \frac{ \frac{1}{4 \pi \epsilon_0} \frac{2 \lambda^2}{R} - \frac{v^2}{c^2} \frac{1}{4 \pi \epsilon_0} \frac{2 \lambda^2}{R} }{\rho} = \frac{ F_e - F_m }{\rho}
The first term in the numerator, F_e \, is the electrostatic force (per unit length) outward and is
reduced by the second term, F_m \, which with a little manipulation, can be shown
to be the classical magnetic force between two lines of charge (or conductors).
The electric current, i_0 \, in each conductor is
i_0 = v \lambda \
and \frac{1}{\epsilon_0 c^2} is the magnetic permeability
\mu_0 = \frac{1}{\epsilon_0 c^2}
because c^2 = \frac{1}{ \mu_0 \epsilon_0 }
so you get for the 2
nd force term:
F_m = \frac{v^2}{c^2} \frac{1}{4 \pi \epsilon_0} \frac{2 \lambda^2}{R} = \frac{\mu_0}{4 \pi} \frac{2 i_0^2}{R}
which is precisely what the classical E&M textbooks say is the magnetic force (per unit length)
between two parallel conductors, separated by R \, with identical current i_0 \.
