Magnetic Forces on a Current-Carrying Wire

fiftysixpowersElectronics - Devices

Oct 18, 2013 (3 years and 7 months ago)

82 views

Magnetic Forces on a Current
-
Carrying Wire


When a wire carries a current in a magnetic field,
there is a force on the wire that is equal to the sum of the
magnetic forces on the charged particles whose motion
produced the current.
























L


The force on this wire in the presence of a magnetic
field B can be written as:


F = ILB sin



Magnetic Field Lines


Just as the electric field, electric
-
field lines can
represent E, the magnetic field can be represented by
magnetic
-
field lines
.



There are two important differences however:


1.

The first has to do with the direction of the force th
e
field exerts on the charge. The electric force on a
positive charge is in the direction of the electric
field, and thus, the electric field line. The magnetic
force is perpendicular to a moving charge so the
field lines are
not
in the direction of the
moving
charge.

2.

The electric field lines began on positive charges
and ended on negative charges. However, because
there are no monopoles, there are no points where
magnetic fields begin or end. Instead they form
closed loops.


The motion of charged parti
cles in a Magnetic Field



The motion of a charged particle in an electric field is
much different than its motion in a magnetic field.














This has many implications and many applications to
areas of medicine, astronomy and nuclear physics.



To
study the applications of particles in magnetic
fields we will try to make an analogy to something you,
hopefully
, already know.


The Force of Gravity



If two massive particles are orbiting each other, such
as the Earth orbiting the Sun,




In what directi
on is the force pointing?



In what direction is the velocity?










F




V






In this scenario, the force and the velocity are
perpendicular
to each other so the Earth will move in a
circle (orbit) around the Sun.


Applic
ation to Magnetic Fields



In order to express things such as forces and velocities
and magnetic fields going into and out of the paper, we will
use the following conventions:



Dots represent a direction out of the page.


Crosses represent motion ou
t of the paper.




Using this convention, please tell me the direction of
the force if a particle is moving to the right of the page and
the magnetic field is pointing into the page:










The force is directed to the “center of the page”!




The circu
lar trajectory and the velocity selector



Recall the equation for the force of a charged particle
moving through a magnetic field:


F = qvB sin




However, as the particle enters the field, the magnetic
force always remains perpendicular to the velocity and is
directed toward the center of the circular path.



To find the radius of the path that the particle will
trace out, recall from mechanics,

the formula for the
centripetal force
:


F = mv
2
/r



Because the force and the velocity are always
perpendicular, sin

= 1 so we can equate the two equations
to find the radius of the path:


r = mv/qB


Why is this important?



One of the most exciting, yip
pee, areas in physics
today is the study of elementary particles, the building
blocks of all types of matter.



Furthermore, it was found at laboratories such as
Fermilab in Batavia Illinois, that the basic protons and
neutrons are made up of even more fun
damental units of
matter called
quarks
.



Even stranger still, Fermilab collides protons into
antiprotons releasing a TREMENDOUS amount of energy.
This energy is able to create strange massive particles such
as muons, pions, etc…



One of the things that
the physicists want to find out is
the charge on these particles. So after they collide, they are
sent into a
bubble chamber
where a magnetic field is set
up. The direction the particle spirals tells the physicist the
charge on that particle.


The Mass
Spectrometer



After a physicist is able to determine the charge on a
particle, the next thing he/she might try doing is to find the
mass of the particle.



Physicists use a mass spectrometer to find the relative
masses of particles and isotopes of element
s.








The mass can be expressed in terms of r, B, and v by
recalling the last equation. By setting values for v and B,
we can measure r and thus find the mass of the particles.



To measure the mass of isotopes of elements, the
electrons are stripped
off the atoms leaving only the
positively charged nucleus. Atoms of higher mass will not
follow the same path.


Sources of Magnetic Fields



We already know that the source of a magnetic field is
moving charge or current. So then we can ask the
questions
:



What type of magnetic fields do wires of different
sizes and shapes produce?



What will be the magnitude of the magnetic field?


To answer this question, we must use the other right hand
rule: Point your thumb in the direction of the current, then
as you
curl your fingers, you are tracing out the direction of
the magnetic field.



For example, what is the direction of the magnetic
field for a straight wire:








The strength of the field is given as:


B =

o

I/2


r


The constant is known as the permeability of free space and
has a value of 4


x 10
-
7
T
-
m/A


Correction from last time, if two wires are carrying a
current in opposite directions, they will
repel
one another
and NOT attract each other.



If you h
ave a loop of wire, what direction is the
magnetic field pointing?






The strength of the field is given as:


B = N (

o

I/2 R)



Where N is the number of “turns” in the loop.








The Solenoid



A solenoid is a long coil of wire in the shape of a
helix
:







The direction of the magnetic field is along the axis of
the solenoid and nearly constant all the way through.


The strength of the field inside is given as:


B =

o

nI



Where n is the number of turns per unit length of the
solenoid and I is the

current.



Solenoids are also referred to as
electromagnets,
and
they have several advantages over permanent magnets. For
one thing, by changing the current in the wire, you can
change the magnetic field.


Application: The MRI



MRI stands for: Magnetic

Resonance Imaging. With
this technique, detailed pictures of the internal structure of
the body can be taken without placing the patient at risk by
exposing them to X
-
rays.



A MRI machine is a huge solenoid and the patient is
inserted into one end of th
e machine.



Inside a huge magnetic field is produced that make the
nuclei of certain atoms to act like tiny radio transmitters
and emit radio waves. The hydrogen atom is made to
behave this way.



With the hydrogens acting in this way, different parts
of

the body can be seen by adjusting the “dial” to the right
“station”. With that, different types of tissue should look a
certain way.



Abnormal tissue, or foreign intruders will look
different than the normal healthy tissue and thus
abnormalities can be
detected.