<< 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

how can chip be made from sand
Eke Reply
are nano particles real
Missy Reply
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
has a lot of application modern world
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
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.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now

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?