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Lorentz force is the electromagnetic force on a point or test charge. The corresponding force law for electromagnetic force is an empirical law providing the combined expression for electrical and magnetic forces experienced by the test charge. Lorentz force for a point charge comes into existence under certain conditions. The existence of either electrical or magnetic or both fields is primary requirement.

The force law sets up the framework under which two force types (electrical and magnetic) operate. The law is fundamental to the study of electromagnetic interactions in terms of field concepts. For the consideration of force(s) on the test charge, the important deduction is that electrical field interacts only with electrical field and magnetic field interacts only with magnetic field. In our context of electromagnetic force, we can say that electrical force results from interaction of two electrical fields and magnetic force results from interaction of two magnetic fields.

Lorentz force expression

The law is stated in vector form as :

F = q [ E + v X B ]

We may recognize that Lorentz force is actually vector sum of two forces :

F = q E + q v X B

For convenience, we refer the first force as Lorentz electrical force and second force as Lorentz magnetic force. The Lorentz electrical force is given by first part as :

F E = q E

The electrical part of law is actually the relation we have already studied in the context of Coulomb’s law and Electrical field. Electrical force on the point charge "q" acts in the direction of electrical field ( E ) and as such the particle carrying the charge is accelerated in the direction of E . If "m" be the mass of the particle carrying charge, then acceleration of the particle is :

a E = F E m = q E m

Lorentz magnetic force is given by second part as :

F M = q v X B

Magnetic force on the point charge "q" acts in the direction perpendicular to the plane formed by v and B vectors. The direction of vector cross product is the direction of magnetic field, provided test charge is positive. The orientation of vector cross product is determined using Right hand thumb rule. If the curl of right hand follows the direction from vector v to B , then extended thumb points in the direction of vector cross product.

Direction of vector cross product

The direction of vector cross product is given by Right hand thumb rule.

We should understand an important point that direction of magnetic field is determined not by the direction of vector cross product vXB alone, but by the direction of expression "q( vXB )". What it means that if charge is negative, then direction of force is opposite to that determined by vector cross product " vXB ". The figure below shows the opposite orientations of vector cross product " vXB " and the magnetic force.

Lorentz magnetic force

Directions of vector cross product and magnetic force are opposite when charge is negative

The acceleration of the particle is given by :

a M = F M m = q v X B m

The magnitude of magnetic force is given by :

F M = q v B sin θ

where θ is the smaller angle between v and B vectors. The magnitude of magnetic field is maximum when θ = 90 or 270 and the maximum value of magnetic field is qvB. It is also clear from the expression of magnitude that magnetic force is zero even when magnetic field exists for following cases :

Questions & Answers

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.
Bharti
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
Daniel
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
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
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
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
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
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.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
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Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
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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