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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

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
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?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
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
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
what is Nano technology ?
Bob Reply
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?
Damian Reply
what king of growth are you checking .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
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?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
hi
Loga
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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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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