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  • Describe the effects of magnetic fields on moving charges.
  • Use the right hand rule 1 to determine the velocity of a charge, the direction of the magnetic field, and the direction of the magnetic force on a moving charge.
  • Calculate the magnetic force on a moving charge.

What is the mechanism by which one magnet exerts a force on another? The answer is related to the fact that all magnetism is caused by current, the flow of charge. Magnetic fields exert forces on moving charges , and so they exert forces on other magnets, all of which have moving charges.

Right hand rule 1

The magnetic force on a moving charge is one of the most fundamental known. Magnetic force is as important as the electrostatic or Coulomb force. Yet the magnetic force is more complex, in both the number of factors that affects it and in its direction, than the relatively simple Coulomb force. The magnitude of the magnetic force     F size 12{F} {} on a charge q size 12{q} {} moving at a speed v size 12{v} {} in a magnetic field of strength B size 12{B} {} is given by

F = qvB sin θ , size 12{F= ital "qvB""sin"θ} {}

where θ size 12{θ} {} is the angle between the directions of v and B . size 12{B} {} This force is often called the Lorentz force    . In fact, this is how we define the magnetic field strength B size 12{B} {} —in terms of the force on a charged particle moving in a magnetic field. The SI unit for magnetic field strength B size 12{B} {} is called the tesla    (T) after the eccentric but brilliant inventor Nikola Tesla (1856–1943). To determine how the tesla relates to other SI units, we solve F = qvB sin θ size 12{F= ital "qvB""sin"θ} {} for B size 12{B} {} .

B = F qv sin θ size 12{B= { {F} over { ital "qv""sin"θ} } } {}

Because sin θ size 12{θ} {} is unitless, the tesla is

1 T = 1 N C m/s = 1 N A m size 12{"1 T"= { {"1 N"} over {C cdot "m/s"} } = { {1" N"} over {A cdot m} } } {}

(note that C/s = A).

Another smaller unit, called the gauss    (G), where 1 G = 10 4 T size 12{1`G="10" rSup { size 8{ - 4} } `T} {} , is sometimes used. The strongest permanent magnets have fields near 2 T; superconducting electromagnets may attain 10 T or more. The Earth’s magnetic field on its surface is only about 5 × 10 5 T size 12{5 times "10" rSup { size 8{ - 5} } `T} {} , or 0.5 G.

The direction of the magnetic force F size 12{F} {} is perpendicular to the plane formed by v size 12{v} {} and B , as determined by the right hand rule 1 (or RHR-1), which is illustrated in [link] . RHR-1 states that, to determine the direction of the magnetic force on a positive moving charge, you point the thumb of the right hand in the direction of v , the fingers in the direction of B , and a perpendicular to the palm points in the direction of F . One way to remember this is that there is one velocity, and so the thumb represents it. There are many field lines, and so the fingers represent them. The force is in the direction you would push with your palm. The force on a negative charge is in exactly the opposite direction to that on a positive charge.

The right hand rule 1. An outstretched right hand rests palm up on a piece of paper on which a vector arrow v points to the right and a vector arrow B points toward the top of the paper. The thumb points to the right, in the direction of the v vector arrow. The fingers point in the direction of the B vector. B and v are in the same plane. The F vector points straight up, perpendicular to the plane of the paper, which is the plane made by B and v. The angle between B and v is theta. The magnitude of the magnetic force F equals q v B sine theta.
Magnetic fields exert forces on moving charges. This force is one of the most basic known. The direction of the magnetic force on a moving charge is perpendicular to the plane formed by v and B size 12{B} {} and follows right hand rule–1 (RHR-1) as shown. The magnitude of the force is proportional to q size 12{q} {} , v size 12{v} {} , B size 12{B} {} , and the sine of the angle between v size 12{v} {} and B size 12{B} {} .

Making connections: charges and magnets

There is no magnetic force on static charges. However, there is a magnetic force on moving charges. When charges are stationary, their electric fields do not affect magnets. But, when charges move, they produce magnetic fields that exert forces on other magnets. When there is relative motion, a connection between electric and magnetic fields emerges—each affects the other.

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
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.
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
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Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
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
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?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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
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what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, College physics ii. OpenStax CNX. Nov 29, 2012 Download for free at http://legacy.cnx.org/content/col11458/1.2
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