streetmeat said:
so what exactly do field lines represent? i still think the tangent of a field line is the direction of the net force.. the vector sum of the forces exerted by 2 charges on a particle in that field. are the lines of equipotential then perpendicular to the field lines?
and about magnetic fields.. a magnetic field is really just an electric field then? i know a stationary charged object creates an electric field, and a moving charge creates a magnetic field.. so maybe a magnetic field is just an electric field that covers a greater distance?
Yes, at every point in space there's a force vector
with a given direction and given magnitude due to
the vector force field. The field lines trace the direction
of these force field vectors to illustrate the shape of the
force field and they can indicate the strength of the field
via various representitve techniques like their spatial
density, their coloring / boldness, annotated numbers,
et. al.
The force vector's magnitude will be relative to some
insignificantly tiny (in all senses) test charge placed
hypothetically at that point in the force field.
So the force field line is drawn along the gradient of
the field potential. As you understand it, the equipotential
lines are contours of constant potential and they are
everywhere at right angles to the force vectors, so moving
a test charge anywhere along an equipotential line will
cause no change in potential for the test charge, and
so no work will be done in moving the test charge along
the equipotential line since it's a 'free ride'.
I'm confused about what you mean by the tangent of the
field line and so on. The field is a vector field and
everywhere at each point in space there's just one
vector which has a specific direction and magnitude
indicative of the force and its direction due to the
force field at that point in space. If you draw contour
lines to illustrate the field's direction (gradient) along
an extended path from any given starting point you'll
end up with a field line that just shows by (running
everywhere in the direction of the gradient) the field's
direction. This would be the case for just one field
source particle, and certainly also so for any number of
other field sources. The field vector at any given
point in space is just the vector sum of the field vectors
from each of the field sources at that point in space,
at least assuming you're in a linear isotropic medium.
The magnetic field is not an electric field and the electric
field is not a magnetic field. A static magnetic field
will cause no acceleration (no force) on a static electric
charge in the static magnetic field.
An electrostatic field MAY exert no net force on a current
loop which is generating a magnetic field if one considers
a case where a large number of infinitesimal equal
and oppositely directed positive and negative charges
are present in the current loop, so there would be no net ELECTRIC charge present over any macroscopic portion
of the current loop (because any volume of the current
loop has equal numbers of positive and negative charges
and they're basically right on top of each other).
However since the positive charges move clockwise
(for the sake of example) and the negative charges move
counterclockwise in this imaginary current loop, there
will be a net magnetic field since their magnetic fields
will sum while their electric fields will cancel.
You really have to study basic relativity and understand
the transitioning from one relativistic reference frame
to another reference frame to see how a single
moving electric charges produce both electric and
magnetic field components when it's viewed from a
frame in which the charge moves.
However when you transform over to a reference frame
in which the charge is stationary (e.g. the observer is
moving along with the charge so the charge seems fixed
in space), you'll 'see' just an electric field and no magnetic
field at all.
This is the essential reason why we say that a charge
density produces the electric field, and why a CURRENT
(CURRENT being DEFINED as MOVING CHARGES)
produces a magnetic field.
So according to Maxwell's equations,
Curl H = J + dD/dt, so if there's no actual current
or displacement current (dD/dt), there's no magnetic
field.
J = current = dQ/dt = the flow of charge in Amperes =
coulombs of charge per second. So if there's no flow of
charge, there's no magnetic field, and the flow of
charge is relative to YOUR motion, just like a boat
flowing quickly down a river may not be in motion relative
to the water it's floating in, but relative to the shore
both the boat and the river are flowing very strongly
along.
