Notes on Relativity and Cosmology - Physics Department, UCSB

44 CHAPTER 2. MAXWELL, E&M, AND THE ETHER
As they grew to understand more and more, physicists found it useful to describe
these phenomena not in terms of the forces themselves, but in terms of things
called “fields”. Here’s the basic idea:
Instead of just saying that X and Y ‘repel’ or that there is a force between
them, we break this down into steps:
• We say that X ‘fills the space around it with an electric field E’
• Then, it is this electric field E that produces a force on Y .
(Electric force on Y ) = (charge of Y )(Electric field at location of Y )
F on Y = q Y E
Note that changing the sign (±) of the charge changes the sign of the force.
The result is that a positive charge experiences a force in the direction of the
field, while the force on a negative charge is opposite to the direction of the
field.
blue = negative charge
red = positive charge
The arrows indicate the field.
Red (positive charge) moves
left with the field. Blue (negative
charge) moves right against
the field.
Similarly, a magnetic charge fills the space around it with a magnetic field B
that then exerts a force on other magnetic charges.
⋆⋆ Now, you may think that fields have only made things more complicated,
but in fact they are a very important concept as they allowed
people to describe phenomena which are not directly related
to charges and forces.
For example, the major discovery behind the creation of electric generators was
Faraday’s Law. This Law says that a magnetic field that changes in time produces
an electric field. In a generator, rotating a magnet causes the magnetic
field to be continually changing, generating an electric field. The electric field
then pulls electrons and makes an electric current.
By the way: Consider a magnet in your (inertial) frame of reference. You, of
course, find zero electric field. But, if a friend (also in an inertial frame) moves
by at a constant speed, they see a magnetic field which ‘moves’ and therefore
changes with time. Thus, Maxwell says that they must see an electric field as
well! We see that a field which is purely magnetic in one inertial frame can have
an electric part in another. But recall: all inertial frames are supposed to yield
equally valid descriptions of the physics.