Resource Lesson
Magnetism: Current-Carrying Wires
Printer Friendly Version
Magnetic fields generated by current-carrying wires
Circular magnetic fields are generated around current carrying wires. The strength of these fields varies directly with the size of the current flowing through the wire and inversely to the distance from the wire.
In this diagram, the solid teal circle in the center represents a cross-section of a current-carrying wire in which the current is coming out of the plane of the paper.
The concentric circles surrounding the wire's cross-section represent magnetic field lines.
The rule to determine the direction of the magnetic field lines is called the
right hand curl rule
.
In this rule, your
thumb
points in the direction of the current
fingers
curl in the direction of
B
The equation to calculate the strength of the magnetic field around a current-carrying wire is:
B
_{perpendicular}
= µ
_{o}
I
/ (2
π
r)
where
µ
_{o}
, permeability of free space = 4
π
x 10
^{-7}
Tm/A
I
, current flowing through the wire, measured in amps
B
, magnetic field strength, measured in Tesla
r, distance from the wire, measured in meters
Refer to the following information for the next two questions.
Determine the magnitude of the current flowing through the wire that is indicated by the grey shaded area.
Determine the direction of the current flowing through the wire.
To examine further details of
Exploration 28.1
authored by Anne J. Cox visit the 2nd edition of Physlet Physics which is hosted by
Compadre
through a
Creative Commons Non-Commercial-NoDerivs 3.0 Unported license
.
Forces on current-carrying wires
When a segment of a current-carrying wire is placed in an external magnetic field, the interaction between the magnetic field of the wire and the external magnetic field is exhibited by a force which is calculated with the formula:
F
=
B
_{perpendicular}
I
L
where
B
is the external, perpendicular magnetic field measured in Tesla,
I
is the current measured in amps, and
L
is the length of the current segment (in meters) that lies in the external magnetic field, B.
The direction of this force also obeys the RHR where your
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
Refer to the following information for the next two questions.
A current-carrying wire having a mass per unit length of 5 grams/cm is levitated between the poles of a permanent horseshoe magnet resting on the top of a demonstration table.
How much current must be running through the wire if the magnetic field has a magnitude of 2 T?
Use the RHR to determine in the picture which side is the north pole: the "front" or the "back?"
Forces between two current-carrying wires
If two current carrying wires are parallel to each other, their respective magnetic fields either attract or repel each other.
As you can see in the diagram above, if two parallel wires have currents traveling in opposite directions, the magnetic fields generated by those currents between the wires will both point in the same direction, in this case, into the plane of the page. These wires would repel each other. An animation showing this result can be view from
MIT's OpenCourseWare.
However, if two parallel wires have currents traveling in the same direction, the magnetic fields generated by those currents between the wires will both point in opposite directions resulting in the wires attracting each other. An animation showing this result can be view from
MIT's OpenCourseWare.
Also notice in the righthand diagram shown below the familiar "ellipses" that we are accustomed to seeing whenever we examine attractive fields. To examine further details of
Exploration 28.2
authored by Anne J. Cox visit the 2nd edition of Physlet Physics which is hosted by
Compadre
through a
Creative Commons Non-Commercial-NoDerivs 3.0 Unported license
.
By using the RHR to determine the direction of the forces their respective magnetic fields exert on each other, we can see that these wires would attract each other.
The formula used to calculate these attractive or repulsive forces is:
F =
B
_{perpendicular}
IL
F
_{12}
=
(µ
_{o}
I
_{1}
/2
π
r) I
_{2}
L
_{2}
F
_{12}
=
(µ
_{o}
/2
π
r) I
_{1}
I
_{2}
L
_{2}
F
_{12}
=
(4
π
x 10
^{-7}
/2
π
r) I
_{1}
I
_{2}
L
_{2}
F
_{12}
=
(2 x 10
^{-7}
/r) I
_{1}
I
_{2}
L
_{2}
where
F
_{12}
represents the force on wire 2 caused by its presence in the magnetic field of wire 1
I
_{1}
is the current flowing in wire 1
I
_{2}
is the current flowing in wire 2
L
_{2}
is the length of the current segment of wire 2 in the field of wire 1
r is the distance between the wires
Refer to the following information for the next two questions.
Two 1-meter long wires are each carrying a current of 2 A but in opposite directions. When the wires are held 10 cm apart,
what is the magnitude of the force that they exert on each other?
are they being attracted or repelled from each other?
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 -
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 -
Electricity and Magnetism Background
RL -
Famous Experiments: Cathode Rays
RL -
Filaments
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 -
Maxwell's Equations
RL -
Meters: Current-Carrying Coils
RL -
Parallel Plate Capacitors
RL -
RC Time Constants
RL -
Torque on a Current-Carrying Loop
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 -
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 -
Exercises on Current Carrying Wires
TB -
Multiple-Battery Circuits
TB -
Textbook Set #6: Circuits with Multiple Batteries
PhysicsLAB
Copyright © 1997-2016
Catharine H. Colwell
All rights reserved.
Application Programmer
Mark Acton