Topic 4.
Magnetic Forces and Fields
Do currents exert forces on each other in the same way that charges do?
Our study of electric forces and electric fields began with a simple experimental
observation: charged particles exert forces on each other. From that, we were able to deduce that
a charged particle creates an "alteration" in space, and that alteration [which we called the
electric field
] exerts a force on any other charged particle that is placed in its presence. We found
that the force exerted by one charge on another gets smaller as their separation increases, but that
the force gets larger as the charge amount increases.
Another simple experimental observation leads to another whole set of physical
phenomena. It is relatively easy to observe that two currentcarrying conductors will exert forces
on each other, even though the conductors do not have any net charge. Since they are not
charged positively or negatively, this new force cannot be the same as the electrical force we
investigated earlier. This new force is due to the influence of
charges on each other.
moving
If one has two
conducting wires of length
placed parallel to each other,
very long
P
carrying currents
and
separated by a distance
, it is found that the magnitude of the mutual
M
M
<
1
2
force exerted by one wire on the other is given by
, where
is a proportionality
J œ +M M PÎ<
+
1
2
constant. If the currents flow in the same direction, the force is attractive. If they flow in opposite
directions, the force is repulsive. It is also observed that if one wire is rotated about its center
point until it is
to the other, there is
on it at all! All in all, a strangely
perpendicular
no net force
different force than the others we have studied in Physics 111 and 112.
In a way that is similar to our previous analysis of electric forces and fields, one can
define a physical entity called the "
" [symbol:
; unit: T (tesla)] that is produced
magnetic field
F
t
by any currentcarrying conductor. This magnetic field is a vector quantity: it has both
magnitude and direction. For a long straight wire, the magnitude of this field depends on the
distance
from the wire, and is given by
, where the same constant
appears as
<
F œ +MÎ<
+
before.
Just as with the analysis of electric fields, we are often interested in the effect of the
magnetic field on some "test" current, and are not interested in (or have no information about)
the source currents that produced the magnetic field. If a test current consisting of a straight wire
of length
carrying current
is placed in a uniform external magnetic field
, then the
P
M
F
magnitude of the force
exerted on that wire is given by
sin
, where
is the angle
J
J œ FMP
)
)
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between the direction of the magnetic field, and the direction in which the current is flowing.
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 Summer '08
 Fretwell
 Charge, Current, Electric Fields, Force, Magnetic Field, 1 m, 2 m, Hans Oersted

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