Some q's about electromagnetism

[streetmeat]

I have a few questions about electromagnetism that no matter how many texts i read i can't seem to figure out, so i'll cut to the chase.

1) why is current in the opposite direction of the flow of electrons? Shouldn't it be in the same direction as the electrons are travelling?

2) How does a current create a magnetic field? I know that 2 charged objects exert a force on each other so I understand how electrical forces work.. what is the difference between an electric field and a magnetic field?

3) If I'm looking at a map of an electric field.. does the tangent of a point on a field line represent the force exerted on a charge at that point? If so how can you ever know the direction a charge will travel if you have to constantly re-evaluate its acceleration? also do the lines represent equal potential energy of the charge.. so does a charge at any point on the same field line have the same amount of potential energy?

also why does electrical field obey an inverse square law to the radius, and a volt is inversely proportional to the radius. i know E = V/r so the math works out but i have trouble visualizing what this means. thanks for the help

 

[ice109]

I have a few questions about electromagnetism that no matter how many texts i read i can't seem to figure out, so i'll cut to the chase.

1) why is current in the opposite direction of the flow of electrons? Shouldn't it be in the same direction as the electrons are travelling?

it is defined as the flow of positive charge, it is because initially when current was discovered people thought charge was positive. negative electrons flowing from right to left is the same thing as positive charge flowing from left to right.

2) How does a current create a magnetic field? I know that 2 charged objects exert a force on each other so I understand how electrical forces work.. what is the difference between an electric field and a magnetic field?

through maxwell's 4 equation. a current creates a magnetic field just like a changing magnetic field creates a current. past that i don't know yet.

3) If I'm looking at a map of an electric field.. does the tangent of a point on a field line represent the force exerted on a charge at that point? If so how can you ever know the direction a charge will travel if you have to constantly re-evaluate its acceleration? also do the lines represent equal potential energy of the charge.. so does a charge at any point on the same field line have the same amount of potential energy?

yes a charge when in a field experiences a force. you don't have to reevaluate it's acceleration, that's what voltage is for. after the particle has traveling some distance along the field line it will have acquired energy and this gives it a kinetic energy. yes you are correct for a non uniform field predicted where and how fast a particle will travel is very difficult. I'm pretty sure computers do it these days. no an equipotential surface is where a particle has the same amount of energy. when you travel along a field line you gain energy( or lose energy ). the point at which you have lost the same amount of energy along another field line, when connected to the first point, make an equipotential.

also why does electrical field obey an inverse square law to the radius, and a volt is inversely proportional to the radius. i know E = V/r so the math works out but i have trouble visualizing what this means. thanks for the help

the e field obeys a square law because ,i don't know it just does. the e=v/r is what I've mentioned before. you could look at it as ExR=V so when you traverse a field line you get a voltage.

 

[waht]

1) why is current in the opposite direction of the flow of electrons? Shouldn't it be in the same direction as the electrons are traveling?

This misconception was conceived in 1750s by Benjamin Franklin who first conducted serious experiments with static electricity. To make long story short, he concluded there exist two kinds of charges and called them positve and negative. He also concluded that one of the charges was stationary, while the other charge was transfered. So he made a hypothesis and designated the moving charge as positive, and stationary charge as negative.

In 1900's J.J. Thompson discovered the electron and for once proved that the negative charge or electron was moving and positive was stationary. But the damage has been done, scientists were used to that convention that positive charge is moving and is still stuck today.

Convention current: when you assume positive charge moves to negative.

In reality it is the negative electrons that are moving.

Scientists and engineers use these conventions interchangeably.2) How does a current create a magnetic field? I know that 2 charged objects exert a force on each other so I understand how electrical forces work.. what is the difference between an electric field and a magnetic field?

Magnetic field is just a relativistic effect of an electric field. The more fundamental field is the electric field. The magnetic field is induced sort of like a tidal force when the electron travels close to speed of light.

3) If I'm looking at a map of an electric field.. does the tangent of a point on a field line represent the force exerted on a charge at that point? If so how can you ever know the direction a charge will travel if you have to constantly re-evaluate its acceleration? also do the lines represent equal potential energy of the charge.. so does a charge at any point on the same field line have the same amount of potential energy?

Sort of confused. The electric field lines represent the strength of an electric field in a give direction. If you place a test charge close to an electric field, the test charge will feel a greatest force in the direction of the biggest arrow.

 

[streetmeat]

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?

 

[xez]

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.