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