Title: Magnetic Moments
1Magnetic Moments
- When you place a loop of wire carrying a current
in a magnetic field, the sections of the wire
that arent parallel to the magnetic field will
experience a force - Remember,
- Since there will be two sides of the loop that
experience opposite forces, a torque is exerted
on the loop!
2Magnetic Moments
The current flows upward in the left arm of the
loop. The force exerted by the magnetic field is
into the page. The current flows downward in
the right side of the loop. The force is out of
the page. The combination is a torque which will
rotate the loop.
3Magnetic Moments
The same situation looking from above the loop.
The current is upward in the left wire and
downward in the right wire. The resulting forces
are shown. Clearly, the loop experiences a
torque which will make the loop rotate.
4Magnetic Moments
As the coil rotates, notice that the effective
moment arm is decreased. This lowers the torque,
although the forces are unchanged.
5Magnetic Moments
6Magnetic Moments
- If we have N turns of wire in the loop
- If the coil makes an angle other than 90o with
the magnetic field, we just throw in a sine term
7Magnetic Moments
- The term NIA is called the magnetic dipole moment
of the coil and is actually a vector - The direction of the area is perpendicular to the
plane of the coil - These ideas are independent of the shape of the
coil and depend only on the area!
8Galvanometers
- We can use the applied torque to measure the
current!!! - The torque is proportional to the current
- Recall Hookes Law for springs
9Galvanometers
The higher the current, the more we twist the
spring and the stronger the resistive torque
becomes. The rotation stops when the two torques
are equal. We can calibrate the pointer position
with the current in the coil, and thus have an
instrument to measure current.
10Galvanometers
- You may have figured out that as the coil turns,
the angle changes and the sine term comes into
play. - To fix this we change the coil in a shrewd way
to take angle out of the picture!!!
11Galvanometers
We curve the poles of the magnet and wrap the
coil around an iron core. The iron concentrates
the field lines and the curve keeps the lines
parallel to the face of the coil!! This takes
angle out of the game.
12DC Motors
Again, we need to be sneaky. When the coil
rotates to the point where the sine is zero, we
need to reverse current direction in the coil,
so we can continue to exert a torque in the same
direction as the rotational inertia keeps the
coil going past that point. See the brushes
which make the connection to the coil!
13The Hall Effect
- The Hall Effect results from the force exerted by
a magnetic field on a moving charge. - We will lock a conductor so it cant move in a
magnetic field. When electrons move through the
conductor, they are forced to one side. This
creates a charge separation and a resulting
electric field.
14The Hall Effect
Electrons move from left to right. The magnetic
field is into the page. The force on the
electron is downward. See the charge separation
in the conductor as positive ions are left behind
on top.
15The Hall Effect
The electrons stop moving when the force of the
electric field is equal to the magnetic force.
This creates a stable configuration with balanced
forces.
16The Hall Effect
- Suppose we have a material in which the charge
carriers are not electrons, but are positively
charged. - We have always said that there is no difference
between negative charges going left to right and
positive charges going right to left when we
deal with currents - NOT TRUE for the Hall Effect
17The Hall Effect
Notice that the Hall EMF is now reversed for
positive charge carriers! Provides a means of
telling what sign a charge carrier has. We will
find positive charge carriers when we deal with
semiconductors.
18The Hall Effect
- Since the Hall EMF is directly proportional to
magnetic field, we can measure the field strength
by measuring the EMF. - The device is called a Hall probe.
- Just calibrate EMF vs. B
19Mass Spectrometry
- Use the magnetic force on a moving charged
particle to separate particles by mass - Useful for analysis and identification
20Mass Spectrometry
Magnetic fields are out of the page. Between
slits for ions with speed v, forces are balanced
between electric and magnetic fields.
qEqvB. All ions out of slit two have the same
speed vE/B. These ions are subject to a force at
right angles to their velocity
21Mass Spectrometry
22Ferromagnetism
- Iron can be permanently magnetized
- Due to alignment of atoms orientation
Regions align all atoms. These are called
domains. Normally, domains are randomly
oriented. Can be aligned with an external
magnetic field and they retain alignment.