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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

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
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for teaching engĺish at school how nano technology help us
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 ?
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.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
how to synthesize TiO2 nanoparticles by chemical methods
what's the program
what chemical
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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