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1: charge is stationary i.e. v=0

2: when charge is moving in the direction of magnetic field or in opposite direction i.e. θ=0 or 180 and sin θ =0.

Further, if only electrical field exists, then only electrical force applies on the point charge and the point charge is accelerated in the direction of electrical field ( E ). If only magnetic field exists, then only magnetic force applies on the point charge except for the cases mentioned above (when magnetic force is zero) and the point charge is accelerated in the direction of vector expression q( vXB ). If both electrical and magnetic field exist, then charge is subjected to both kinds of force provided conditions for zero magnetic force are not met. In the last case, acceleration of the point charge is in the direction of resultant force :

a = F m = q [ E + v X B ] m

Problem : An electron, moving along x-axis in an uniform magnetic field B , experiences maximum magnetic force along z-axis. Find the direction of magnetic field.

Solution : Since the particle experiences maximum magnetic force, the angle between velocity and magnetic field vector is right angle. Now, magnetic force in z-direction is also perpendicular to the magnetic field. Hence, magnetic field is either in positive or negative y-direction. By applying Right hand rule of vector cross product, we find that it is oriented in positive y-direction if the charge is positive. But, charge on electron is negative.

Lorentz magnetic force

Orientations of direction of vector cross product and magnetic force

Hence, magnetic field is oriented along negative y-direction.

Nature of magnetic force

The nature of magnetic force is different to electrical force. First, it is not linear in the sense that it does not operate in the direction of magnetic field. This is unlike electric force which acts in the direction of applied electric field. The magnetic force, as we have seen in the preceding section, acts in the side-way direction following vector cross product rule. Also, magnetic force is relatively weaker as magnetic field is a weaker field in comparison with electric field.

The first of the two distinguishing characteristics as described above has important implications. Since magnetic force is perpendicular to the direction of velocity, it can only change the direction of motion – not its magnitude. The magnetic force can not change the magnitude of velocity i.e. speed of the charged particle. In turn, we can say that magnetic force can not bring about a change in the kinetic energy of the charged particle as speed remains same due to magnetic field.

An immediate fall out of the magnetic force is very interesting. This force does no work. We know work is scalar dot product of force and displacement. Now, velocity is time rate of displacement. It means velocity and displacement have same direction. Since magnetic force is perpendicular to velocity, it is also perpendicular to small elemental displacement. What it means that magnetic force is always perpendicular to displacement. Thus, work done by magnetic force is zero.

Questions & Answers

Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
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s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
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what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
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types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
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what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
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I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
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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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