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e E = e v B v = E B

Note that maximum magnetic force applies as velocity and magnetic field vectors are perpendicular to each other. Substituting expression of v in the kinetic energy equation obtained earlier, we have :

m E 2 B 2 = 2 e V α = e m = E 2 2 V B 2

All the quantities on the right hand side of the equation are measurable, allowing us to measure the specific charge of electron. As a matter of fact, the determination of specific charge of particles composing cathode ray by J.J.Thomson is considered to be the discovery of electron. It can also be easily inferred that he could determine the nature of charge of an electron by studying direction of deviation (upward or downward) when only either of the fields operate. In the derivation above, we measure potential difference applied to accelerate particle between cathode and anode. We should, however, realize that we can determine specific charge measuring some other quantities as well. We can measure the deflection of electron beam when either of two fields operates and use the data to determine specific charge of an electron.

Problem : The d.c. voltage applied to accelerate particle between cathode and anode and the d.c. voltage applied to the plates to produce electric field perpendicular to electrons beam are equal in the Thomson’s experimental set up. If each of the two d.c. voltages as applied are doubled, then by what factor should the magnetic field be changed to keep the electron beam un-deflected.

Solution : Let V 1 , E 1 and B 1 be the potential difference, electric field and magnetic field for un-deflected condition. Then, the specific charge is given by :

α = e m = E 1 2 2 V 1 B 1 2

Here, the electric field can be expressed in terms of potential difference provided we know the separation between plates. Let the separation be d.

E 1 = V 1 d

Putting in the equation above, we have :

α = V 1 2 2 d 2 V 1 B 1 2 = V 1 2 d 2 B 1 2

Let B 2 be the new magnetic field when two potential differences as applied are doubled. Here,

V 2 = 2 V 1

Putting new values in the expression for specific charge (note that specific charge of electron is a constant),

α = 2 V 1 2 d 2 B 2 2

Combining two equations,

2 V 1 2 d 2 B 2 2 = V 1 2 d 2 B 1 2 2 V 1 d 2 B 2 2 = 4 V 1 d 2 B 1 2 B 2 2 B 1 2 = 2 B 2 B 1 = 2

Measurement of deflection by magnetic field

Once the magnetic and electric forces are balanced, electric field is switched off and electron beam is allowed to be deviated due to magnetic field. The magnetic force acts always perpendicular to the direction of motion. The particle, therefore, moves along a circular path inside the region of magnetic field. When electron moves out of the magnetic field, it moves along the straight line and hits the fluorescent screen. If R be the radius of curvature, then :

m v 2 R = e v B m v = e R B

Substituting v = E / B as obtained earlier

α = e m = E R B 2

We measure R using geometry. We see that the angles enclosed between pairs of two perpendicular lines are equal. Hence,

J.j.thomson’s experimental set up

Deviation due to only magnetic field

φ = D G R = O I F O R = F O X D G O I

We approximate DG to be equal to the width of magnetic region.

Measurement of deflection by electric field

In this case, once the magnetic and electric forces are balanced, electric field is switched off and electron beam is allowed to be deviated due to electric field. The electron beam moving into the region of electric field experiences an upward force. The force in upward (y-direction) imparts acceleration in y-direction. The particle, however, moves with same velocity in x-direction. As a result, path of motion is parabolic. Let the length of plate be L and y be the deflection inside the plate. Then, time to travel through the plate is :

J.j.thomson’s experimental set up

Deviation due to only electric field

t = L v

and acceleration of the particle in y-direction is :

a y = F E m = e E m

The vertical displacement is :

y = 1 2 a y t 2

Substituting for time and acceleration, we have :

y = 1 2 X e E m X L 2 v 2 = e E L 2 2 m v 2

Substituting v=E/B as obtained earlier,

y = e E L 2 2 m X B E 2 = α E L 2 2 X B E 2 α = e m = 2 y E B 2 L 2

It is clear that measuring GH and HI, we can determine angle φ and then y as required.

Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
how can I make nanorobot?
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Electricity and magnetism. OpenStax CNX. Oct 20, 2009 Download for free at http://cnx.org/content/col10909/1.13
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