Chapter 21. Magnetic Forces and Fields. Magnetism Magnetic Force and Field Trajectory of a Charge in a Magnetic Field Magnetic Forces and Torques on Electric Currents Magnetic Fields Produced by Currents Ampere’s Law Magnetic Materials. Chapter 21: Magnetic Forces and Fields. Magnetism.
Magnetic Forces and Fields
Magnetic Force and Field
Trajectory of a Charge in a Magnetic Field
Magnetic Forces and Torques on Electric Currents
Magnetic Fields Produced by Currents
Magnetic MaterialsChapter 21: Magnetic Forces and Fields
The unity of physics:
Magnesia: now called “Manisa,” in western Turkey
Here, around 500 BC, people first noticed that a particular sort of iron ore, suspended from a thread, sought a constant orientation relative to the earth.
No isolated poles (instead, opposed pairs: dipoles)
N & S (“north” and “south”)
Unlike poles attract each other
Like poles repel each other
Pole names result from tendency toward geographic alignment
The “north” pole is the end of a magnetic dipole that seeks the geographic north direction on Earth.
The magnetic field is a vector that points from a magnetic north pole, toward a magnetic south pole.
The field points in the same direction as the north pole of a compass needle.
Magnetic field lines point toward a south magnetic pole.
The magnetic field vector is tangent to the field line at each point.
The magnetic field vector is mathematically defined from its property of exerting a force on a moving charge.
The magnetic force on a moving charge:
Direction: given by right-hand rule #1
Right-hand rule #1, two ways:
The magnetic force equation serves as a defining equation for the magnetic field, B:
SI units of magnetic field, B: (tesla)
Other common unit of B: the gauss ( = )
Serbian-American inventor and electrical engineer
1856 - 1943
German mathematician and physicist
1777 - 1855
Properties of the magnetic force on moving charges
The magnetic force does no work on the moving charge?
Consider a charged object moving at a velocity v in a plane perpendicular to a uniform magnetic field B:
The magnetic force on the charge is always perpendicular to its velocity.
At a later time, the force is still perpendicular to the velocity.
A force that always acts on an object perpendicular to its velocity is a centripetal force.
This force produces circular motion. (Recall Chapter 5.)
The force, velocity, and path radius are related by:
But FC is also the magnetic force:
If ions have a mass m and a charge q:
Recall the magnetic force on a charge moving perpendicular to a magnetic field:
Now, if a current I flows through a straight wire whose length is L:
q is now the angle between the field vector B and the wire
The direction of F is still given by right-hand rule #1
(the thumb is now the conventional current)
Maximum torque occurs when f = 90° (plane of coil is parallel to B):
Minimum torque occurs when f = 0° (plane of coil is perpendicular to B):
Experimental observation (due to Oersted): a current-carrying wire produces a magnetic field, directly proportional to the magnitude of the current, and inversely proportional to the distance from the wire:
Convert to an equation, using a constant of proportionality:
m0 is called the permeability of free space:
Danish physicist; discovered the field due to a current- carrying wire by accident, one evening in April 1820, while preparing for a lecture at the University of Copenhagen
Direction: right-hand rule #2
Each wire produces a magnetic field at the location of the other wire
Each wire experiences a magnetic force due to the field produced by the other
RHR #2 shows that the magnetic field points out of the plane of the loop on the inside of the loop, and into the plane on the outside of the loop.
The field magnitude is not uniform.
The field magnitude at the center is given by:
If the loop becomes a flat coil, with N turns:
Solenoid: a coil whose length is large compared to its radius.
Field magnitude inside the solenoid:
# of turns per unit length
For an arbitrary closed path about an arbitrary current distribution I:
We can also write this as a sum of “sufficiently” small length elements around the closed path:
Ampere’s Law can be used to calculate the magnetic fields produced by simple current geometries. Example: the long straight wire:
Right-hand rule #2 says that B
is everywhere parallel to Dl. So:
Electrons have orbital and spin rotations in atoms.
These circular motions of charge act as current loops, and produce magnetic dipoles on an atomic scale.
These magnetic dipoles mostly cancel each other. The remaining dipoles tend to be oriented randomly, so bulk materials do not show magnetic dipole behavior.
In ferromagnetic materials (iron, cobalt, nickel, and some alloys), there is a spin coupling of some electrons over small portions of the material called domains.
The domains do behave as magnetic dipoles.
In an “ordinary” object made of a ferromagnetic material, the domains are themselves randomly oriented, and the object is not a magnet.
The ferromagnetic domains may be brought into a common alignment by an external magnetic field (induced magnetism).
In some materials, the common domain alignment is persistent, even when the external field is removed. The object is then a permanent magnet.
The ferromagnetic field can be several orders of magnitude higher than the external field that causes the domain alignment.