Sources of Magnetic Fields

2wireAni.gif (13870 bytes)

Two parallel wires carrying currents in the same direction attract each other.  Ba is the magnetic field at wire b produced by the current in wire aFba is the resulting force acting on wire b because it carries current in field Ba.

2wirefrontview.gif (2557 bytes)

In this figure, the system of two current carrying wires is viewed in the direction of the currents.  With the currents perpendicular to the plane of the drawing and directed "into" the plane, the magnetic field created by current ia circulates along (is tangent in clockwise direction to) circles centered at current a.   The figure shows the direction of this magnetic field Ba at the location of current ib.

Previously Asked Questions

Q:     Is the magnetic field generated by a current loop uniform?

A:    No, the magnetic field depends on the position in space where it is measured.  Textbooks and engineering handbooks and manuals usually give only the formula for the magnetic field created by a current loop, as measured at different positions on the axis of symmetry, x, of the loop.  Of course, a particular case would be the case where x = 0, and this simplified formula would give the magnetic field in the center of the loop.   In order to obtain the value of the magnetic field created by a current loop at any point is space (outside the axis of symmetry), one should integrate the contributions of each element of current at the given position in space.  Such an integration is possible, but it is somewhat more tedious than for points situated on the axis, because of lack of symmetry of the problem.

Q:    When two parallel wires carry current in opposite directions, the wires move apart.  Shouldn't they move closer together since opposites attract?

A:    Don't rush to transport into science (physics) any general knowledge you have from life outside the school (as reflected in everyday words or phrases).  In physics, it is true that two static electric charges with opposite sign ( positive and negative ) attract.  Also, two static opposite magnetic poles ( North and South ) attract.  Maybe, two people with opposite personality traits attract.  But, two parallel wires carrying currents in opposite direction do not attract, they repel.  In the case of two charges or two magnetic poles, there is a force of interaction oriented in the direction that connects the two charges or two poles.  The magnitude of this force is given by the Coulomb's Law.  In the case of currents, the force of interaction is obtained by considering not static charges but the charges moving through the wires forming the two currents.   The electrons in one current move in the field created by the second current, and vice-versa, the electrons in the second current move in the field created by the first current.  For each charge moving in an electric field, the force applied by the field on the charge is given by the formula F = q ( v x B ).  The magnitude of this force is F = q v B ( sin theta2.gif (833 bytes) ), where theta2.gif (833 bytes) is the angle between velocity v and magnetic field B.   Since the direction of motion of electrons in one current is perpendicular to the magnetic field created by the second current (which is in the shape of circles around centered around the current), it follows than theta2.gif (833 bytes) = 90 degrees and sin theta2.gif (833 bytes) = 1.  The direction of this force, as given by the formula above, is the direction the cross product v x B and is therefore perpendicular to both v and B.   Its direction is toward the second current.  Correct estimation of the direction of this interaction force shows that the force is attractive for two currents that are parallel and in the same direction, and is repulsive for two currents that are parallel and in opposite direction.

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The Biot-Savart Law: The contribution dB to the field produced by a current-length element i ds at point P, a distance r from the current element, is:
30-5.gif (284 bytes)

The permeability constant (mu2.gif (832 bytes)0) has the value 4pi2.gif (831 bytes)  x 10 -7  T . m/A  approx.gif (53 bytes) 1.6 x 10 -6  T . m/A

Formulas and Equations

Biot-Savart Law 30-5.gif (284 bytes)
Force between parallel wires carrying current 30-14.gif (421 bytes)
Ampere's Law 30-16.gif (218 bytes)
Magnetic field of a long straight wire 30-6.gif (175 bytes)
Field of an ideal solenoid B = mu2.gif (832 bytes)0 i n
Field of a toroid 30-26.gif (224 bytes)
Field of a magnetic dipole 30-29.gif (246 bytes)

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List of Topics

Measurements Electric Potential Magnetism Electrical Circuits (AC) Optical Instruments: Mirrors and Lenses
Electrostatics Capacitance Sources of Magnetic Fields Maxwell's Equations Interference
Electric Fields Current and Resistance Magnetism in Matter Electromagnetic Waves Diffraction
Electric Flux Electrical Circuits (DC) Electromagnetic Induction Interaction of Radiation with Matter: Reflection, Refraction, Polarization