Electricity and Magnetism 101
of defining the current is due to the historical accident that Benjamin
Franklin defined a current as a flow of positive charge at least one
hundred years before the electron was actually discovered. Although
there is a current due to the drift of the electrons, the wire itself is
electrically neutral. If one examines a given section of a wire, as much
charge flows out of it as into it. The force observed between wires
carrying currents is therefore not due to the electric force but some other
force.
It was also discovered that an electric current exerts a force on a
magnetic compass. In fact, one can make an artificial magnet by
wrapping copper wire around an iron bar and passing a current through
the wire. It is clear from these two experiments that an electric current
behaves like a magnet and that the force between two electric currents is
magnetic. Further study showed that the magnetic force, like the electric
force, is also inversely proportional to the square of the distance between
the two currents. Since the current in a wire has a net charge of zero, one
cannot ascribe the magnetic force solely to the charge of the particles
within. It is clear that it is the motion of the charge particles that
produces this new force, which differs from the electric force in a
number of ways.
Perhaps the best way of comparing the two forces is to consider the
interaction of two positively charged particles moving parallel to each
other. There is a repulsive electric force between these two charges
whose strength is proportional to the product of their charges divided by
the square of the distance between. In addition to this electric force there
is also an attractive magnetic force whose strength is also proportional to
the product of the charges divided by the square of the distance between
them. The magnetic force is also proportional, however, to the product of
their velocities divided by the velocity of light squared. Since the
velocity of a particle can never be greater than the velocity of the light,
the magnetic force is always less than the electric force.
The force depends on the relative direction of the two currents in a
complicated fashion. When the two currents are parallel (anti-parallel)
the force is attractive (repulsive). The force acts along the line
connecting the two currents and is equal and opposite. For other
configurations, the force is not always directed along the line connecting
the two currents and it is not always equal and opposite.
The connection between the magnetic properties of an electric current
and a lodestone or magnet is easily made by considering the atomic