This experiment mirrors that a cathode ray is consisted of of pposts with a constant proportion of charge to mass ( e/m ). A magnetic area bends the cathode rays right into a closed circle.

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Apparatus and Materials

Fine beam tube and standPower supply, 0-250V (High Tension, HT), via distinct shrouded connecting leads6.3V supply for the heater filament (this is regularly included on the EHT supply)Demonstration meters, 2DC dial: 5 ampDC dial: 300 voltsHall probeHelmholtz coilsPower supply, low voltage, variable, 0 - 12V OR Battery load, 6V, 2 & Rheostat

Health & Safety and also Technical Notes

Make all relationships with the power supply off.

Connecting leads supplied for the HT volteras should have actually enough insulation.

The HT supply deserve to provide a fatal existing. Use 4 mm leads via plugs having sprung shrouds for all high-voltage connections. The teacher supervising in a darkened room have to be aware of the dangers and their control.

Do not connect or disaffix leads as soon as the HT is switched on.

Read our standard health & safety and security guidance

The easiest means to measure the magnetic area stamina is to use a Hall probe. These are obtainable from most devices manufacturers. They come as a stand-alone unit which provides a digital read-out of magnetic field toughness.

Hall probe sensors are additionally available via some computer interfaces – as among the sensors that plugs right into the interconfront. If you currently have among these interchallenge kits, this might be a cheaper option than a stand-alone Hall probe.

For this experiment, students don’t necessarily should know just how the Hall probe works – you can present it ssuggest as a maker for measuring magnetic area stamina.

A Teltron-form tube works finest for this demonstration because you can usage the electron gun that sends out out a vertical beam. This have the right to then be bent into a complete circle.

Follow the manufacturer’s instructions for establishing up the fine beam tube.


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Encertain that you can identify the following:

The 6.3V supply to the cathode heater (if you connect the wrong voltage to the heater you deserve to quickly damages the tube beyond repair).The HT supply to the anode. Set this to zero. The negative terminal of the HT goes to a socket, which is regularly near to the heater terminals.

A tube which has not been provided for a while might not emit electrons. It may be possible to encourage it to carry out so by raising the heater voltage by roughly 1V or so. Monitor it closely. Encertain that the normal heater present is just slightly gone beyond.

Procedure

Setting up...

It is best to meacertain the magnetic field from the coils prior to setting up the tube. Set up the coils without the fine beam tube – one on each side of wright here the tube will be. Connect them in series via each various other, via the ammeter and via the 12-volt power supply (or battery, rheostat and the switch).Set the existing in the coils to about 2.5 amps.Use the Hall probe to meacertain the magnetic area.
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Switch the coils off for now. Do not adjust the rheostat or power supply from currently on.Set up the fine beam tube in its distinct stand also.Select the gun which provides a vertical electron beam. (There may be a selection switch.) Connect the 6.3 V supply to the filament. (Some HT gives accessible for school use incorporate this output. Additionally, it is possible to usage a sepaprice low voltage transformer.)Connect the negative terminal of the HT supply to the filament and also the positive terminal to the anode.Connect a voltmeter between the anode and cathode in order to meacertain the speeding up voltage, which need to be around 250 volts.Carrying out... Set the HT voltage to zero and also switch on the 6.3 V supply to the heater filament.When the filament is glowing, very closely boost the anode voltage. At a voltage, which may be as low as 50 volts, it should be possible to see the fine beam. As the voltage is progressively boosted, the beam will certainly lengthen and strike the glass envelope of the tube. Switch on the current to the coils. The beam should be bent into a circular course.

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Adsimply the speeding up voltage till the beam forms a complete circle inside the tube – coming earlier about on itself. (Do not readjust the current in the coils unmuch less you really have to. If you do readjust it, you will certainly should meacertain the area again).Increasing and decreasing the accelerating voltage on the electron gun will show how the radius of the course of the electrons varies via the rate of the electrons for a consistent magnetic area. The faster the electrons, the even more difficult they are to bend, so the radius of the path rises.Each team of pupils should measure the course diameter D and also the increasing voltage. To measure D, ssuggest organize a ruler exterior the tube. In the darkened room, the leader should be illuminated. (A Perspex leader via a tiny electrical lamp taped to one finish - and also covered through masking tape so that no straight light emerges – functions well.)Increasing the existing with the field coils for a constant voltage on the electron gun will certainly display just how the circular route of the electrons changes via the strength of the magnetic field. The more powerful the magnetic area, the more result it has actually on the electrons and the circular route reduces in radius. If you adjust the present in the field coils, be certain you rerotate it to the worth at which you measured the field strength.

Teaching Notes

This experiment is best demonstrated to the students in groups of 4 to five in a darkened room if full worth is to be obtained.Always alleviate the anode voltage to zero once not actually observing the beam because the tube has actually a finite life time.The electron beam is visible bereason tbelow is a low-press gas in the tube. Electrons striking the gas molecules carry energy; the molecules then emit light. Hydrogen gas glows blue and helium gas glows green. It is worth reminding students of the catapult field on a existing delivering wire prior to showing the deflection of electrons. (See Related Experiments, below.) In the situation of the magnetic pressure on a beam of electrons we need to change the expression from the pressure of a magnetic field on a present delivering wire into the pressure of a magnetic field on a relocating charge. Given that the beam is made of electrons, the direction of the existing is in the direction of the cathode.The force F on a wire of size L transporting current I in a magnetic area B is F = ILB.Here I = e / t and also v = L / t, where e is the electron charge and also v is its rate.So F = evBIn the fine-beam tube the catapult force of the magnetic field is perpendicular to the stream of negatively charged electrons and so a unidevelop magnetic area will host the stream in a circular orbit provided the electrons move at a continuous rate. The magnetic field pulls the electrons right into an orbit rather choose a tether that holds a whirling round.If the tube is twisted slightly in its holder then the circular activity of the beam combines with a direct component of the beam to make a spiral.It is useful if students practise measuring the diameter of the beam by measuring the diameter of a wire loop without being allowed to carry the wire loop close to to the rule. Practice through the loop will certainly conserve time as soon as they all meacertain the beam diameter.The best alteration so far developed creates a virtual photo of an illuminated scale inside the tube, in the aircraft of the electron stream. To do this, area a vertical sheet of clean plate glass simply in front of the tube. Place an illuminated range in front of the sheet at such a distance that the picture of the range, behind the sheet, is in the middle of the tube. This does make dimensions easier; however we perform not recommend including this complication other than via an extremely able group.The focus is to carry students into call via real experiments on electrons and not to concern too a lot around precision, which may be past the design of the apparatus. Students must be motivated to devise refinements, such as measuring the diameter of the electron beam, but too many type of refinements will make the experiments incredibly facility and the easy elegance of it will certainly be lost.When JJ Thomboy measured the worth of e/m he did not have the deluxe of a heated cathode producing electrons all at the very same speed, and also so he did not know the rate of the electrons. He had to deflect his beam of electrons through a magnetic field and also then return them to their undeflected position via an electrical area. It is worth stating through students what they can infer from this experiment (and what they can’t).The fact that the cathode rays are deflected mirrors that they have charge; the direction of the deflection shows the charge is negative (which was currently assumed because they arised from a cathode).The fact that they are deflected in a curved path and also not deflected via a best angle reflects that they have inertia or mass. From this, we assume that the cathode ray is comprised of pposts.The reality that the totality beam is preserved undamaged reflects that the particles are all deflected by the very same amount.It is most likely that the beam is comprised of pwrite-ups that are all the same. But, at this stage, we cannot infer this for specific.We can infer that the ratio of the charge to mass of all the particles is the very same. If there are some pwrite-ups in the beam that have actually twice the charge, they should also have actually twice the mass. This is bereason they all follow the exact same orbit; the radius of the orlittle counts on the acceleration. In revolve, the acceleration counts on the pressure on the pposts and their mass. The doubled charge will cause the force to be twice as huge however the doubled mass will expect that the acceleration is the very same. Using the outcomes to discover e/m (the particular charge):The electrons are accelerated in an electric field. Increasing the accelerating voltage boosts the rate of the electrons. Energy that was stored in the electrical field (electrical potential energy) is now stored kinetically. SoIncrease in kinetic energy = decrease in electric potential energy1/2 mv2 = e V (equation 1)where m is the mass of the electron, e its charge, v its velocity and also V the speeding up voltageThese moving electrons enter the magnetic area created by the coils. This bends them into a circular orbit.The magnetic pressure, F , on the electrons is provided byF = B e v where B is the magnetic field toughness, e is the charge on the electron and v their speedGiven that the electrons are going in a circle, we understand that this force must have actually a dimension ofmv2 / r wbelow m is the mass of the electron and r is the radius of the orlittle bit.So you can say that:B e v = mv2/ rso B e = mv / r (equation 2)There are two ways you could usage these equations via students. The first is algebraic and the second uses values for the rate. The first is even more finish. However before, you might desire to usage the second so as not to distract students from the achievement of measuring properties of the electron.Algebraic approach:Combining equations 1 and 2 will certainly result in the equation:e/m = 2V/B2r2 from which students might calculate worths of e/mor r2 = 2Vm/eB2 from which students could plot a graph of r2 against V and also uncover e/m from the gradient.Using worths for speed:A simple resetup of equation 2 gives,r = mv/BeSo a graph of r (radius) versus v (speed) will certainly yield a value for e/m. However, you cannot calculate the rate from equation 1 (without separately learning e/m). However before, you deserve to use the table below to give students the (non-relativistic) speeds at different volteras. These are correct to within 1%. Gun Voltage/V 100
Speed of Electrons/m/s
6×106
1408×106
1808×106
2309×106
28510×106
The embraced worth of e/m is 1.76 x 1011 C/kg.You will perform well to get a result that is the correct order of magnitude. Tright here are fairly big uncertainties in the radius dimensions and also some uncertainty in the measurement of the magnetic area toughness. Both of these quantities are squared in the algebraic strategy.Knowing that the charge on an electron, e = 1.6 x 10-19 Coulomb from Millikan’s experiment, along with the value for e / m = 1.76 x 1011 C/kg leads to a value of 9 x 10-31 kg for the mass of the electron. The very same value of e / m is found for all electrons, whatever before their source – warm filaments of metals, the photoelectrical effect, bombarding gases by electrons, electric areas tearing atoms apart and even nuclei emitting beta pposts. This proof leads scientists to mean that electrons are global ingredients of matter, all the same.A equivalent calculation for the proton, with charge e = 1.6 x 10-19 Coulomb and also e / M = 9.6 x 107C/kg leads to a value of 1.67 x 10-27 kg for the mass of a proton.

This experiment was security checked in March 2008