Resource Lesson
Torque on a Current-Carrying Loop
Printer Friendly Version
Remember that when a current-carrying wire is placed in an external magnetic field then it will experience a
magnetic force
that can be calculated with the equation
and obeys the right hand rule.
thumb points in the direction of the current, I
fingers point in the direction of the external magnetic field, B
palm faces the direction of the force, F
This
physlet by Walter Fendt
illustrates this Lorentz force.
Example #1:
Now let's place a freely-pivoting loop carrying a clockwise (red arrow) current in an external (+x) magnetic field.
as the current flows up the left side, it will experience a force in the -z direction.
as the current flows across the top of the loop, no force is exerted since the current and the magnetic field are parallel.
as the current flows down the right side, it will experience a force in the +z direction.
These forces will result in the right side of the loop rotating towards the reader.
Example #2:
Now let's place the same freely-pivoting loop carrying a clockwise (red arrow) current in an external (+z) magnetic field.
as the current flows up the left side, it will experience a force in the +x direction.
as the current flows across the top of the loop, it will experience a force in the -y direction
as the current flows down the right side, it will experience a force in the -x direction.
Since the lines of action of both forces along the vertical sides pass through the axis of rotation they will not produce a torque. Note that the line of action of the force along the top section of the loop runs parallel to the axis and consequently can also not produce a torque.
In this orientation, the coil will not rotate about the specified axis.
Every current-carrying coil has an
area vector
,
A
, that is oriented perpendicular to is cross-sectional area and points in the direction dictated by the right hand curl rule:
I
circulates clockwise
A
points in the -z direction
B
points in the +x direction
the right edge of the coil would
rotate towards the reader
I
circulates counter-clockwise
A
points in the +z direction
B
points in the +x direction
the right edge of the coil would
rotate away from the reader
aerial view
aerial view
Take a moment and investigate the following
physlet modeling the rotation
of the current-carrying loop in a magnetic field by Dr. Scott at Lawrence Technological University in Southfield, Michigan. Notice how the direction/magnitude of the current, direction/magnitude of the magnetic field and the size of the angle between the magnetic moment (area vector) affect the loop's rotation.
When the area vector is at right angles to the magnetic field the torque is maximized. Conversely, when the area vector is parallel to the magnetic field no torque is produced as evidenced in our second introductory example.
So how do we calculate the magnitude of the torque on a current-carrying coil?
Returning to our initial example,
We see that the torque
can be calculated using the appropriate values for
r
and
F
as
If there was more than one loop, the expression would be multiplied by the number of loops, N.
The expression NIA is called the
magnetic moment
of the loop and it measured in Am
^{2}
. Although we have derived this equation for a rectangular loop, it can be used with any planar loop of any geometry - in particular, circular loops whose areas are
.
Refer to the following information for the next three questions.
Suppose you have a circular loop of radius 0.25 meters that has 100 turns of wire. The coil carries 2 amps of current while in a magnetic field having a magnitude of 10 T.
What is the coil's magnetic moment?
What is the maximum torque the coil experiences?
Which would have a greater effect: reducing the radius by a factor of 2 or reducing the number of loops by a factor of 2?
To see an application of the torque on a current-carrying loop, investigate this
physlet
by Walter Fendt of an electric DC motor.
Related Documents
Lab:
CP -
Series and Parallel Circuits
Labs -
Forces Between Ceramic Magnets
Labs -
Magnetic Field in a Solenoid
Labs -
Mass of an Electron
Labs -
Parallel and Series Circuits
Labs -
RC Time Constants
Labs -
Resistance and Resistivity
Labs -
Resistance, Gauge, and Resistivity of Copper Wires
Labs -
Telegraph Project
Labs -
Terminal Voltage of a Lantern Battery
Labs -
Wheatstone Bridge
Resource Lesson:
RL -
A Comparison of RC and RL Circuits
RL -
A Guide to Biot-Savart Law
RL -
A Special Case of Induction
RL -
Ampere's Law
RL -
An Introduction to DC Circuits
RL -
Capacitors and Dielectrics
RL -
Dielectrics: Beyond the Fundamentals
RL -
Eddy Currents plus a Lab Simulation
RL -
Electric Field Strength vs Electric Potential
RL -
Electricity and Magnetism Background
RL -
Famous Experiments: Cathode Rays
RL -
Filaments
RL -
Inductors
RL -
Introduction to Magnetism
RL -
Kirchhoff's Laws: Analyzing Circuits with Two or More Batteries
RL -
Kirchhoff's Laws: Analyzing DC Circuits with Capacitors
RL -
LC Circuit
RL -
Magnetic Field Along the Axis of a Current Loop
RL -
Magnetic Forces on Particles (Part II)
RL -
Magnetism: Current-Carrying Wires
RL -
Maxwell's Equations
RL -
Meters: Current-Carrying Coils
RL -
Parallel Plate Capacitors
RL -
RC Time Constants
RL -
RL Circuits
RL -
Spherical, Parallel Plate, and Cylindrical Capacitors
Worksheet:
APP -
Maggie
APP -
The Circuit Rider
APP -
The Cycle Shop
APP -
The Tree House
CP -
DC Currents
CP -
Electric Power
CP -
Magnetism
CP -
Ohm's Law
CP -
Parallel Circuits
CP -
Power Production
CP -
Power Transmission
CP -
RIVP Charts #1
CP -
RIVP Charts #2
CP -
Series Circuits
NT -
Bar Magnets
NT -
Brightness
NT -
Light and Heat
NT -
Magnetic Forces
NT -
Meters and Motors
NT -
Parallel Circuit
NT -
Series Circuits
NT -
Shock!
WS -
Capacitors - Connected/Disconnected Batteries
WS -
Combinations of Capacitors
WS -
Induced emf
WS -
Introduction to R | I | V | P Charts
WS -
Kirchhoff's Laws: DC Circuits with Capacitors
WS -
Kirchhoff's Laws: Sample Circuit
WS -
Magnetic Forces on Current-Carrying Wires
WS -
Magnetic Forces on Moving Charges
WS -
Practice with Ampere's Law
WS -
Resistance, Wattage, and Brightness
TB -
34A: Electric Current
TB -
35A: Series and Parallel
TB -
36A: Magnets, Magnetic Fields, Particles
TB -
36B: Current Carrying Wires
TB -
Advanced Capacitors
TB -
Basic Capacitors
TB -
Basic DC Circuits
TB -
Electric Field Strength vs Electric Potential
TB -
Exercises on Current Carrying Wires
TB -
Multiple-Battery Circuits
TB -
Textbook Set #6: Circuits with Multiple Batteries
PhysicsLAB
Copyright © 1997-2019
Catharine H. Colwell
All rights reserved.
Application Programmer
Mark Acton