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Magnetic Force. PH 203 Professor Lee Carkner Lecture 16. Charge Carriers. Imaging a current flowing from top to bottom in a wire, with a magnetic field pointing “in” If the charge carriers are negative (moving to the top), the magnetic field will also deflect them to the right. - PowerPoint PPT Presentation
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Charge Carriers
Imaging a current flowing from top to bottom in a wire, with a magnetic field pointing “in”
If the charge carriers are negative (moving to the top), the magnetic field will also deflect them to the right
The Hall Effect
If it is high the carriers are positive
Since a voltmeter shows the
low potential is on the right, the electron is negative
Hall Quantified
Electrons are now longer deflected and the potential across the strip is constant
but the velocity is the drift speed of the electrons
v = i/neA
n = Bi/eAE Since the potential V = Ed and the thickness of
the strip (lower case “ell”), l = A/dn = Bi/Vle
Electric and Magnetic Force
For a uniform field, electric force vector does not change
Electric fields accelerate particles, magnetic fields deflect particles
Particle Motion
A particle moving freely in a magnetic field will have one of three paths, depending on
Straight line When =
Circle When =
Helix When
This assumes a uniform field that the particle does not escape from
Circular Motion
This will change the direction of v, and change the direction of F towards more bending
How big is the circle? Magnetic force is F = Centripetal force is F =
We can combine to getr = mv/qB
Radius of orbit of charged particle in a uniform magnetic field
Circle Properties
Circle radius is inversely proportional to q and B
r is directly proportional to v and m
Can use this idea to make mass spectrometer
Send mixed atoms through the B field and they will come out separated by mass
Helical Motion
Charged particles will spiral around magnetic field lines If the field has the right geometry, the particles can become
trapped
Since particles rarely encounter a field at exactly 0 or 90 degrees, such motion is very common
Examples: Gyrosynchrotron radio emission from planets and stars
Magnetic Field and Current
We know that i = q/t and v = L/t (where L is the length of the wire)
So qv = iL, thus:F = BiL sin
We can use the right hand rule to get the direction of
the force Use the direction of the current instead of v
Force on a Loop of Wire
Consider a loop of wire placed so that it is lined up with a magnetic field Two sides will have forces at right angles to
the loop, but in opposite directions The loop will experience a torque
Torque on Loop
Since = 90 and L = h,F = Bih
The torque is the force times the moment arm (distance to the center), which is w/2
but hw is the area of the loop, A
= iBA
= iBA sin
General Loops
= iBAN sin he torque is maximum when the loop is aligned with the field
and zero when the field is at right angles to the loop (field goes straight through loop)
If you reverse the direction of the current at just the right time you can get the coil to spin
Can harness the spin to do work
A beam of electrons is pointing right at you. What direction would a magnetic field have to have to produce the maximum deflection in the right direction?
A) Right
B) Left
C) Up
D) Down
E) Right at you
A beam of electrons is pointing right at you. What direction would a magnetic field have to have to produce the maximum deflection in the up direction?
A) Right
B) Left
C) Up
D) Down
E) Right at you