Chapter 10 Magnetic Fields:Ill a The lorentz force Example: The Closed-Field Mass Spectrometer Example: The hall Effect Example: Magnetic Mirrors
Chapter 10 Magnetic Fields:III ◼ The Lorentz Force ◼ Example: The Closed-Field Mass Spectrometer ◼ Example:The Hall Effect ◼ Example:Magnetic Mirrors
10.1 The Lorentz force Experiments show that a charged particle moving in a magnetic field experiences a force F=Q(v×B) Q- the charge of the particle, the velocity of the particle(vector) B-the magnetic field If there is also an electric field the force acting on the e particle is F=Q(E+v×B)
Example: The Closed-Field Mass Spectrometer See Fig 10-1 The positive ions originate from the source s at a potential V. Passing between the plates, the ion beam splits vertically according to its mass
For the ion going from the source s to the deflect ing plates, the potential energy is converted into the kinetic energy mv=QV 2 Between the plates the electric field e is upward the electric force Qe Is upward the magnetic field b is towards us, the magnetic force Qvx B is downward If the net force on th e ion is zero F=Q(E+v×B) E B
Plugging this v=b into the relation amv<=QV gIves B m=2QV a particle with this mass will not be affected by the electromagnetic field between the plates, and will be arrive at the collector C, and the ammeter will show the current When this happens, we can tell the mass m, since he values B, E,V, and Q are known from the experiment
Example: The hall Effect See Fig 10-2(b )and(d )for an n-type semiconductor the electrons as charge carriers a bar of semiconductor is placed in a transverse mag- netic field B A current I flows through the bar B oVx BE (b)
When the electrons flows with a velocity v to form a current I, they experience a magnetic force Fm =QuB directing downward So the electrons drift downward and accumulate at the lower portion of the bar Thus an electric field Ey forms, directing downward and the electrons experience an electric force Fe=QE directing upward
When Fe= Fm, (balanced ) the electrons stop drift ing. We e have Ey oB This electric field is called the hall field The corresponding potential is V= Enb- bb
Example: Magnetic Mirrors See Fig 10-4 for a give magnetic field a proton goes toward the left, spiraling around the magnetIc line(x-a×ls
The magnetic field is approximately K B at the corner(ao, zo)of the dashed lines, it is simply B=(roi+ zok The velocity of the proton at(e0, 2o) is given by Vo=v00j+002k Note that here 000<0, and v0z <0 The Lorentz force acting on the proton is K F=e(v B)=e(voej+v02k)x(aoi+ zok)3