The relationship between magnetism
and electricity is very close. This page is dedicated to how magnetism
and electricity interact in fields but before we discuss that I
feel it is important to know a little bit about the electromagnetic
force.
According to this
physics page "[the electromagnetic force] one of the four
fundamental forces the electromagnetic force manifests itself
through the forces between charges (Coulomb's Law) and the magnetic
force, both of which are summarized in the Lorentz force law."
The lorentz force is is given by this equation:
![](pictures/lorfor.JPG)
(Images Courtesy of http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfor.html#c2)
Below is the explanation of the variables.
![](pictures/lorfor2.JPG)
Now that we know how closely related
the electric and magnetic forces are it is appropriate to discuss
further the interaction between electricity and magnetism in fields.
The first interaction is a magnetic
force acting on a current carrying wire. This situation acts similar
to the situation of a charged particle moving through a magnetic
field. There is a force on the wire. It is simply a collection of
charges in motion. "Hence the resultant force exerted by the
field on the wire is the vector sum of the individual forces exerted
on all the charged particles making up the current" (Serway).
The total Magnetic force on a wire is equal to the current(I) times
L(length of wire) cross B(magnetic field). If we have a closed current
loop the net magnetic force acting on it is 0. The magnetic field
of an electric current is shown below in a picture:
![](pictures/magcur.JPG)
(Image courtesy of http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magcur.html#c1)
As you can see in the picture above the right hand
rule is applicable. You put your thumb in the direction of the current
and your curled fingers is the magnetic field.
Soon after Oersted's discovery that
a compass needle is reflected by a current-carrying wire two scientist
by the name of Jean-baptiste Biot and Felix Savart performed experiments
dealing with the force exerted by a current on a nearby magnet (Serway).
Their experiments lead to the Biot-Savart law. "The Biot-Savart
Law relates magnetic fields to the currents which are their sources"(source).
The Bio-Savart Law is explained in the image below.
(Images courtesy of http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/biosav.html#c1)
There are variants of magnetic fields
and wires. Ampere's
law can be used in many of these variants. See Ampere's
law applications.
The last subject I will touch on here
is Electromagnetic Fields. Electromagnetic waves (which naturally
involve magnetic fields and electric fields) are predicted by Maxwell's
equations. These equations are I. Gauss' law for electricity
II. Gauss' law for magnetism III. Faraday's law of induction IV.
Ampere's law .
The electromagnetic spectrum is given
by the image below.
![](pictures/emus.JPG)
The reason I mentioned the electromagnetic
fields is so we could discuss the energy in electric and magnetic
fields. We know both fields store energy. Electric fields store
energy in capacitors and magnetic fields store energy in inductors.
The equations for the energy densities are shown below.
![](pictures/engef.JPG)
Above is energy density for electric fields
(Images Provided by http://hyperphysics.phy-astr.gsu.edu/hbase/electric/engfie.html#c1)
Below is energy density for magnetic fields
![](pictures/engbf.JPG)
These equations, as you may have noticed, are very
closely related. One will very quickly discover that magnetism and
electricity are very related fields. They share many of the same
rules and equations just slightly modified, and their interaction
with each other is outstanding.
![](pictures/emwavec.JPG)
(Image courtesy of http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)
The Infamous Electromagnetic
Wave "Dance"!
As you can probably see magnetism
and electricity are very extensive and closely related fields. I
find the properties of magnets and magnetic fields to be fascinating.
The integral role both areas play in our daily lives and the theory
of physics is mind boggling. It really is too extensive to cover
completely but the site below does an excellent job.
This page is the ultimate source on Electricity and Magnetism(http://hyperphysics.phy-astr.gsu.edu/hbase/emcon.html#emcon)
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