# 0.8 Motion of a charged particle in electric and magnetic fields  (Page 3/4)

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$y=\frac{1}{2}{a}_{y}{t}^{2}=\frac{1}{2}\alpha E{t}^{2}$

The position vector of the particle after time t is :

$\mathbf{r}=x\mathbf{i}+yj+z\mathbf{k}$ $⇒\mathbf{r}=\frac{{v}_{0}}{\alpha B}\mathrm{sin}\left(\alpha Bt\right)\mathbf{i}+\frac{1}{2}\alpha E{t}^{2}\mathbf{j}+\frac{{v}_{0}}{\alpha B}\left[1-\mathrm{cos}\left(\alpha Bt\right)\right]\mathbf{k}$

## Charge is placed at rest in crossed electric and magnetic fields

Let electric and magnetic fields are aligned along z and x directions and charge is placed at the origin of coordinate system. Initially, there is no magnetic force as charge is at rest. However, there is electric force, which accelerates the charge in z-direction. As the particle acquires velocity in z-direction, the magnetic force comes into play and tries to rotate the particle in xz plane about a center on x-axis.

However, z-component of velocity keeps increasing with time due to electric force in that direction. The magnetic force though draws the charged particle away from z-axis along a curved path. This action of magnetic force is countered by electric force in z-direction. The velocity of charged particle ultimately reduces to zero at x-axis. This cycle repeats itself forming cycloid motion. The cycloid path is generated by a point on the circumference of a rolling wheel. Here, we shall skip the mathematical derivation and limit ourselves to a descriptive analysis only.

## Determination of specific charge of electron (j.j.thomson’s experiment)

The specific charge of an electron is ratio of charge and mass of electron. The specific charge (α) of electron is measured employing crossed fields on a beam of electrons. The beam of electrons emerging from cathode plate passes through a very narrow slit in anode plate. The electrons are accelerated between cathode and anode due to applied electrical potential V. The kinetic energy of the electron emerging from the slit is given by :

$\frac{1}{2}m{v}^{2}=eV$ $⇒m{v}^{2}=2eV$

where v is the velocity of electron moving into the region of force fields.

Two parallel plates connected to an electric source produce a uniform electric field E from positive plate to negative plate. The electrical force works in the direction opposite to the direction of field E as charge on electron is negative. In the figure, electric field is directed in downward direction. Hence, electric force acts in upward direction.

On the other hand, the magnetic field is produced by a solenoid in a circular region covering the plate as shown in the figure. Its direction is chosen such that it applies a force in the opposite direction to that applied by the electrical field. For a magnetic field into the plane of drawing as shown by uniformly distributed cross signs, the magnetic field applies a upward magnetic force on a positive charge. However, as the charge on the electron is negative, the magnetic force acts in downward direction.

The beam of electrons hit the center of fluorescent screen, producing light as electrons collide with it when electric and magnetic fields are switched off. The point on the fluorescent screen is noted. Then, the electric field is switched on which moves the electron beam in upward direction following a parabolic path. Finally, magnetic field is turned and its magnitude is adjusted such that electric and magnetic forces acting in opposite directions balance each other and the electron is brought to hit original spot as noted earlier for the fields in switched off condition. In this situation:

what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
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
Rafiq
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
how did you get the value of 2000N.What calculations are needed to arrive at it
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