Physics Tutorial Qns on Electromagnetism

jaydunkfull

3 Apr 08, 03:57

please help me! i suck at physics. im doing a tutorial on electromagnetism now and ive got 3 qns. thanks for any help

1) A beam of electrons whose kinetic energy is K emerges from a thin foil window at the end of an accelerator tube. There is a metal plate a distance d from this window and perpendicular to the direction of the emerging beam. Show that we can prevent this beam from hitting the plate if we apply a uniform magnetic field of flux density B such that B> (2mk/e^2d^2)^0.5

2) A cyclotron is an accelerator in which a beam of energetic particles is produced. The charged partilces describe a spiral path of many turns at right angles to a constant magnetic field and are given an acceleration always in the same sense from an alternating electric field, each time they cross the gap between the two conductors ( dees). These charged particles then leave the cyclotron at the outer edge. Note that within the Dees, the charged particles are shielded from the electric fields by the copper walls of the Dees

a) if the charged particles were protons explain clearly how the alternating electric field provides the acceleration

b) show that the frequency of the applied voltage is independent on the radius of the orbit

c) show that the kinetic energy gained per cycle is 2qV where V is the magnitude of the voltage applied but V does not affect the final energy of the charged particles.

there are diagrams for each of the qns but i cant insert them. can anyone tell me how to insert the diagrams??

thanks!

Darkness_hacker99

3 Apr 08, 07:29

Use a free hosting site. eg. photobucket

Once you obtained your image link, come back here and click the 'tree' icon.

Paste the link, then insert.

-*:+:MUSE:+:*-

3 Apr 08, 07:41

please do so. draw diagrams for us.

jaydunkfull

4 Apr 08, 01:35

ive inserted the images. but somehow the first one cant be displayed. hmm :(

eagle

5 Apr 08, 12:57

I guess for question 2, wiki should answer most of your queries. I shall post the more relevant parts here... The diagram in your question isn't very self-explanatory...

Diagram of cyclotron operation from Lawrence's 1934 patent.

The electrodes shown above would be in the vacuum chamber, which is flat, in a narrow gap between the two poles of a large magnet.

In the cyclotron, a high-frequency alternating voltage applied across the "D" electrodes (also called "dees") alternately attracts and repels charged particles. The particles, injected near the center of the magnetic field, accelerate only when passing through the gap between the electrodes. The perpendicular magnetic field (passing vertically through the "D" electrodes), combined with the increasing energy of the particles forces the particles to travel in a spiral path.

With no change in energy the charged particles in a magnetic field will follow a circular path. In the Cyclotron, energy is applied to the particles as they cross the gap between the dees and so they are accelerated (at the typical sub-relativistic speeds used) and will increase in mass as they approach the speed of light. Either of these effects (increased velocity or increased mass) will increase the radius of the circle and so the path will be a spiral.

(The particles move in a spiral, because a current of electrons or ions, flowing perpendicular to a magnetic field, experiences a perpendicular force. The charged particles move freely in a vacuum, so the particles follow a spiral path.)

The radius will increase until the particles hit a target at the perimeter of the vacuum chamber. Various materials may be used for the target, and the collisions will create secondary particles which may be guided outside of the cyclotron and into instruments for analysis. The results will enable the calculation of various properties, such as the mean spacing between atoms and the creation of various collision products. Subsequent chemical and particle analysis of the target material may give insight into nuclear transmutation of the elements used in the target.

Mathematics of the cyclotron

The centripetal force is provided by the transverse magnetic field B, and the force on a particle travelling in a magnetic field (which causes it to be angularly displaced, i.e spiral) is equal to Bqv. So,

$\frac{mv^2}{r} = Bqv$

(Where m is the mass of the particle, q is its charge, v is its velocity and r is the radius of its path.)

The speed at which the particles enter the cyclotron due to a potential difference, V.

$v = \sqrt{\frac{2Vq}{m}}$

Therefore,

$\frac{v}{r} = \frac{Bq}{m}$

v/r is equal to angular velocity, ω, so

$\omega = \frac{Bq}{m}$

And since the angular frequency is

ω = 2π f c

Therefore,

$f_c = \frac{Bq}{2m\pi}$

This shows that for a particle of constant mass, the frequency does not depend upon the radius of the particle's orbit. As the beam spirals out, its frequency does not decrease, and it must continue to accelerate, as it is travelling more distance in the same time. As particles approach the speed of light, they acquire additional mass, requiring modifications to the frequency, or the magnetic field during the acceleration. This is accomplished in the synchrocyclotron.

The relativistic cyclotron frequency is

$f=f_c\sqrt{1-v^2/c^2}$ ,

where $f c$ is the classical frequency, given above, of a charged particle with velocity $v$ circling in a magnetic field.

The rest mass of an electron is 511 keV, so the frequency correction is 1% for a magnetic vacuum tube with a 5.11 kV direct current accelerating voltage. The proton mass is nearly two thousand times the electron mass, so the 1% correction energy is about 9 MeV, which is sufficient to induce nuclear reactions.

An alternative to the synchrocyclotron is the isochronous cyclotron, which has a magnetic field that increases with radius, rather than with time. The de-focusing effect of this radial field gradient is compensated by ridges on the magnet faces which vary the field azimuthally as well. This allows particles to be accelerated continuously, on every period of the radio frequency, rather than in bursts as in most other accelerator types. This principle that alternating field gradients have a net focusing effect is called strong focusing. It was obscurely known theoretically long before it was put into practice.

eagle

5 Apr 08, 13:04

Question 1

A beam of electrons whose kinetic energy is K emerges from a thin foil window at the end of an accelerator tube. There is a metal plate a distance d from this window and perpendicular to the direction of the emerging beam. Show that we can prevent this beam from hitting the plate if we apply a uniform magnetic field of flux density B such that B> (2mk/e^2d^2)^0.5

A magnetic field can only cause the moving beam of electrons to move in a circular path. Without the size of the metal plate, the direction of the magnetic field, and the picture to further explain other things to us, it is not really possible to give an answer without many many assumptions.

In addition, is the k in B> (2mk/e^2d^2)^0.5 referring to the kinetic energy K?
'K' is very different from 'k' in physics.

Do try posting the picture again. You could try in a new post, or post the link to the picture