Chapter 28 Sources of Magnetic Field

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SOURCES OF MAGNETIC FIELDSections we will coverMagnetic Field of a Moving ChargeMagnetic Field of a Current ElementMagnetic Field of a Straight Current-Carrying ConductorForces Between Parallel ConductorsMagnetic Field of a Circular Current LoopAmperes LawApplications of Amperes Law28

The magnetic field of a moving chargeWe are familiar with the force caused by a permanent magnet, but even that magnetic field arises from the motion of charges within atoms. So lets look at the force caused by a single moving charge and build up from there. Experiments show that the magnetic field, B, is proportional to the amount of charge, q, and inversely proportional to the square of the distance from the charge, r. That is very similar to the results found for the electric field. Unlike the electric field however, the magnetic field depends on the velocity of the charge, v. Also the direction of the magnetic field is not radially along r, but is perpendicular to both r and v. Mathematically this is expressed as:

Experiments yield the proportionality constant, so that we have the magnetic field caused by a single charge moving with constant velocity to be:

is a unit vector in the radial direction

The magnetic field of a moving chargeBecause B is perpendicular to v and r, the field does not radiate outward like an electric field, but forms concentric circles around the moving charge:

The outer loops would have a smaller B field by the inverse square nature of B.

A positive point charge is moving directly toward point P. The magnetic field that the point charge produces at point PA. points from the charge toward point P.B. points from point P toward the charge.C. is perpendicular to the line from the point charge to point P.D. is zero.E. The answer depends on the speed of the point charge.

Question4Magnetic force between moving protonsSo, if you had two single charges moving near each other, what would the total force be on one due to the other? Consider the case of two protons moving with the same speed in opposite but parallel directions:

The B field at the upper proton caused by the lower proton is:

So the force is:

Which is repulsive, as is the Coulomb force:

The ratio of these forces is:

c = the speed of light in a vacuum, but also, c2=1/eomo due to the interdependence of E and B fieldsFB < FE for v