PhysicsLAB: Magnetism: Current-Carrying Wires

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_oI / (2πr)

where

µ_o, permeability of free space = 4π 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} IL

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
F₁₂ =	(µ_oI₁/2πr) I₂L₂
F₁₂ =	(µ_o/2πr) I₁I₂L₂
F₁₂ =	(4π x 10^-7/2πr) I₁I₂L₂
F₁₂ =	(2 x 10^-7/r) I₁I₂L₂

where

F₁₂ represents the force on wire 2 caused by its presence in the magnetic field of wire 1
I₁ is the current flowing in wire 1
I₂ is the current flowing in wire 2
L₂ 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?