Learning Objectives. Book Reference : Pages 113-115. Charged Particles In Circular Orbits. To understand that the path of a charged particle in a magnetic field is circular To equate the force due to the magnetic field to the centripetal force
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
Book Reference : Pages 113-115
To understand that the path of a charged particle in a magnetic field is circular
To equate the force due to the magnetic field to the centripetal force
To examine practical applications of circular particle displacement
In the previous lesson we have seen that a moving charged particle is deflected in a magnetic field in accordance with Fleming’s left hand rule
Magnetic field coming out of the page
Initial Path of the Electron
The force on the moving charged particle is always at right angles to the current velocity... Circular motion!
A beam of electrons with a velocity of 3.2x107 m/s is fired into a uniform magnetic field which has a flux density of 8.5mT. The initial velocity is perpendicular to the field.
Explain why the electrons move in a circular orbit
Calculate the radius of the orbit
What must the flux density be adjusted to if the radius of the orbit is desired to be 65mm
Charge on an electron (e) = -1.6 x 10-19 C
Electron rest mass (me)= 9.11 x 10-31 kg
However it also quotes...
Electron Charge/Mass ratio(e/me) = 1.76x1011 C/kg
Two things.... Do not be phased by this since they could quote this for another particle... Simply inverting it (m/Q) for this sort of calculation saves one step in the calculator!
Such devices can also be called
The cathode is a heated filament with a negative potential which emits electrons, a nearby positive anode attracts these electrons which pass through a hole in the anode to form a beam. This is called Thermionic emission. The potential difference between the anode and cathode controls the speed of the electrons.
These are machines which can be used to analyse the types of atoms, (and isotopes) present in a sample
r = mv/BQ
The key to how it works is the effect that the mass has on the radius of the circular motion while keeping the velocity and flux density constant
First we need to ionise the atoms in the sample so that they become charged... Electrons are removed yielding a positive ion
A component known as a “velocity selector” is key to obtaining a constant velocity
The +ve ions are acted upon by both an electric field & a magnetic field.
Only when they are equal & opposite do the ions pass through the slit
The electric field is given by F = QV/d & the magnetic field given by F = BQv Only ions with a particular velocity will allow QV/d = BQv & hence only ions with that particular velocity make it through the slit. Note that it is also independent of charge since the Qs cancel
Cyclotrons are a method of producing high energy beams used for nuclear physics & radiation therapy
An alternating electric field is used to accelerate the particles while a magnetic field causes the particles to move in a circle, (actually a spiral since the velocity is increasing)
Compared to a linear accelerator, this arrangement allows a greater amount of acceleration in a more compact space
Two hollow D shaped electrodes exist in a vacuum. A uniform magnetic field is applied perpendicular to the plane of the “Dees”
Charged particles are injected into a D, the magnetic field sets the particle on a circular path causing it to emerge from the other side of this D & to enter the next.
As the particle crosses the gap between the Ds the supplied current changes direction (high frequency AC) & the particle is accelerated, (causing a larger radius)