Electric current creates a magnetic field, the reverse
effect also exists: magnetic fields, in turn, can influence electric charges
and cause electric currents to flow. However, there is an important twist: the
magnetic field must be changing in order to have any effect.
A static magnetic field, such as a bar magnet, will not
cause any motion of nearby charge. Yet if there is any relative motion between
the charge and the magnetic field—for example, because either the magnet or the
wire is being moved, or because the strength of the magnet itself is changing—
then a force will be exerted on the charge, causing it to move.
This force is called an electromotive force (emf) which,
just like an ordinary electric field, is distinguished by its property of
accelerating electric charges. The most elementary case of the electromotive
force involves a single charged particle traveling through a magnetic field, at
a right angle to the field lines (the direction along which iron filings would
line up).
This charge experiences a force again at right angles to
both the field and its velocity, the direction of which (up or down) depends on
the sign of the charge (positive or negative) and can be specified in terms of
another right-hand rule, as illustrated in Figure 1.3.
This effect can be expressed concisely in mathematical terms
of a cross product of vector quantities (i.e., quantities with a directionality
in space, represented in boldface), in what is known as the Lorentz equation, F
= ¼ qv X B where F denotes the force, q the particle’s charge, v its velocity,
and B the magnetic field.
In the case where the angle between v and B is 908 (i.e.,
the charge travels at right angles to the direction of the field) the magnitude
or numerical result for F is simply the arithmetic product of the three
quantities. This is the maximum force possible: as the term cross product
suggests, the charge has to move across the field in order to experience the
effect.
The more v and B are at right angles to each other, the
greater the force; the more closely aligned v and B are, the smaller the force.
If v and B are parallel—that is, the charge is traveling along the magnetic
field lines rather than across them—the force on the charge is zero. Figure 1.3
illustrates a typical application of this relationship.
The charges q reside inside a wire, being moved as a whole
so that each of the microscopic charges inside has a velocity v in the
direction of the wire’s motion. If we align our right hand with that direction
v and then curl our fingers in the direction of the magnetic field B (shown in
the illustration as pointing straight back into the page), our thumb will point
in the direction of the force F on a positive test charge.
Because in practice the positive charges in a metal cannot
move but the negatively charged electrons can, we observe a flow of electrons
in the negative or opposite direction of F.
Because only the relative motion
between the charge and the magnetic field matters, the same effect results if
the charge is stationary in space and the magnetic field is moved (e.g., by
physically moving a bar magnet), or even if both the magnet and the wire are
stationary but the magnetic field is somehow made to become stronger or weaker
over time.
The phenomenon of electromagnetic induction occurs when this
electromagnetic force acts on the electrons inside a wire, accelerating them in
one direction along the wire and thus causing a current to flow. The current
resulting from such a changing magnetic field is referred to as an induced
current.
This is the fundamental process by which electricity is
generated, which will be applied over and over within the many elaborate
geometric arrangements of wires and magnetic fields inside actual generators.
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