<< Chapter < Page Chapter >> Page >
  • Describe the effects of a magnetic force on a current-carrying conductor.
  • Calculate the magnetic force on a current-carrying conductor.

Because charges ordinarily cannot escape a conductor, the magnetic force on charges moving in a conductor is transmitted to the conductor itself.

A diagram showing a circuit with current I running through it. One section of the wire passes between the north and south poles of a magnet with a diameter l. Magnetic field B is oriented toward the right, from the north to the south pole of the magnet, across the wire. The current runs out of the page. The force on the wire is directed up. An illustration of the right hand rule 1 shows the thumb pointing out of the page in the direction of the current, the fingers pointing right in the direction of B, and the F vector pointing up and away from the palm.
The magnetic field exerts a force on a current-carrying wire in a direction given by the right hand rule 1 (the same direction as that on the individual moving charges). This force can easily be large enough to move the wire, since typical currents consist of very large numbers of moving charges.

We can derive an expression for the magnetic force on a current by taking a sum of the magnetic forces on individual charges. (The forces add because they are in the same direction.) The force on an individual charge moving at the drift velocity v d is given by F = qv d B sin θ . Taking B size 12{B} {} to be uniform over a length of wire l and zero elsewhere, the total magnetic force on the wire is then F = ( qv d B sin θ ) ( N ) size 12{F= \( ital "qv" rSub { size 8{d} } B"sin"θ \) \( N \) } {} , where N size 12{N} {} is the number of charge carriers in the section of wire of length l size 12{l} {} . Now, N = nV size 12{N= ital "nV"} {} , where n size 12{n} {} is the number of charge carriers per unit volume and V size 12{V} {} is the volume of wire in the field. Noting that V = Al size 12{V= ital "Al"} {} , where A size 12{A} {} is the cross-sectional area of the wire, then the force on the wire is F = ( qv d B sin θ ) ( nAl ) . Gathering terms,

F = ( nqAv d ) lB sin θ . size 12{F= \( ital "nqAv" rSub { size 8{d} } \) ital "lB""sin"θ} {}

Because nqAv d = I size 12{ ital "nqAv" rSub { size 8{d} } =I} {} (see Current ),

F = IlB sin θ size 12{F= ital "IlB""sin"θ} {}

is the equation for magnetic force on a length l of wire carrying a current I in a uniform magnetic field B , as shown in [link] . If we divide both sides of this expression by l , we find that the magnetic force per unit length of wire in a uniform field is F l = IB sin θ size 12{ { {F} over {l} } = ital "IB""sin"θ} {} . The direction of this force is given by RHR-1, with the thumb in the direction of the current I size 12{I} {} . Then, with the fingers in the direction of B size 12{B} {} , a perpendicular to the palm points in the direction of F size 12{F} {} , as in [link] .

Illustration of the right hand rule 1 showing the thumb pointing right in the direction of current I, the fingers pointing into the page with magnetic field B, and the force directed up, away from the palm.
The force on a current-carrying wire in a magnetic field is F = IlB sin θ size 12{F= ital "IlB""sin"θ} {} . Its direction is given by RHR-1.

Calculating magnetic force on a current-carrying wire: a strong magnetic field

Calculate the force on the wire shown in [link] , given B = 1 . 50 T size 12{B=1 "." "50"" T"} {} , l = 5 . 00 cm size 12{l=5 "." "00"" cm"} {} , and I = 20 . 0 A size 12{I="20" "." 0 A} {} .


The force can be found with the given information by using F = IlB sin θ size 12{F= ital "IlB""sin"θ} {} and noting that the angle θ size 12{θ} {} between I size 12{I} {} and B size 12{B} {} is 90º , so that sin θ = 1 .


Entering the given values into F = IlB sin θ size 12{F= ital "IlB""sin"θ} {} yields

F = IlB sin θ = 20 .0 A 0 . 0500 m 1 . 50 T 1 . size 12{F= ital "IlB""sin"θ= left ("20" "." 0" A" right ) left (0 "." "0500"" m" right ) left (1 "." "50"" T" right ) left (1 right )} {}

The units for tesla are 1 T = N A m size 12{"1 T"= { {N} over {A cdot m} } } {} ; thus,

F = 1 . 50 N. size 12{F=1 "." "50"" N"} {}


This large magnetic field creates a significant force on a small length of wire.

Magnetic force on current-carrying conductors is used to convert electric energy to work. (Motors are a prime example—they employ loops of wire and are considered in the next section.) Magnetohydrodynamics (MHD) is the technical name given to a clever application where magnetic force pumps fluids without moving mechanical parts. (See [link] .)

Diagram showing a cylinder of fluid of diameter l placed between the north and south poles of a magnet. The north pole is to the left. The south pole is to the right. The cylinder is oriented out of the page. The magnetic field is oriented toward the right, from the north to the south pole, and across the cylinder of fluid. A current-carrying wire runs through the fluid cylinder with current I oriented downward, perpendicular to the cylinder. Negative charges within the fluid have a velocity vector pointing up. Positive charges within the fluid have a velocity vector pointing downward. The force on the fluid is out of the page. An illustration of the right hand rule 1 shows the thumb pointing downward with the current, the fingers pointing to the right with B, and force F oriented out of the page, away from the palm.
Magnetohydrodynamics. The magnetic force on the current passed through this fluid can be used as a nonmechanical pump.

A strong magnetic field is applied across a tube and a current is passed through the fluid at right angles to the field, resulting in a force on the fluid parallel to the tube axis as shown. The absence of moving parts makes this attractive for moving a hot, chemically active substance, such as the liquid sodium employed in some nuclear reactors. Experimental artificial hearts are testing with this technique for pumping blood, perhaps circumventing the adverse effects of mechanical pumps. (Cell membranes, however, are affected by the large fields needed in MHD, delaying its practical application in humans.) MHD propulsion for nuclear submarines has been proposed, because it could be considerably quieter than conventional propeller drives. The deterrent value of nuclear submarines is based on their ability to hide and survive a first or second nuclear strike. As we slowly disassemble our nuclear weapons arsenals, the submarine branch will be the last to be decommissioned because of this ability (See [link] .) Existing MHD drives are heavy and inefficient—much development work is needed.

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
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
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
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, General physics ii phy2202ca. OpenStax CNX. Jul 05, 2013 Download for free at http://legacy.cnx.org/content/col11538/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'General physics ii phy2202ca' conversation and receive update notifications?