This is a most interesting scientific puzzle. I had
been unsuccessful in getting my point over during a discussion with a university
physics professor, so I posed the following puzzle, which I asked him to
solve. Although it seemed to me to be comparatively simple, he refused,
saying it was a "trick". In my opinion, the rather simple puzzle
described below can be solved with just a basic knowledge of physics.
Puzzle: In order to solve this problem, one
must have a basic knowledge of the properties of an electric dipole
(defined by Coulomb's Law), which is simply two separated
positive and minus charges in open space, as shown below:
The distances from each of the two electric charges
to the origin are equal, and therefore the distances from the charges to
any point in the y-z plane are also equal. At any point to
the right of the y-z plane the field is negative, and at any
point to the left it is positive. Therefore, the field level is zero
everywhere in the y-z plane.
I now pose the question as to what happens to
the shape of the zero-field level planar shape (the y-z
plane) as the entire system is moved toward the left? It is not necessary
to consider exact values, just the general shape of the plane wave, or even
just a vertical line within it, in the far field. Considering just
the vertical line through the origin, does its shape change, or
does it remain straight? If it changes shape, then plot the general shape
at some short time, T, after the system is moved. For convenience
and simplicity, limitations of inertia need not be imposed (start and stop
times). If you have difficulty in visualizing the situation, make a guess.
The import of the results are highly significant.
Conditions and Suggestions : Simply move the
dipole (both charges) directly to the left at a uniform velocity and neglect
the rise and fall times. The distance between the charges does not
change. Does the shape of the plane (or vertical line in the plane) bend,
or does it stay straight? If it bends, then think about how it bends. Hint:
consider the limitations of the speed of light and the conditions in the
far field. You may be surprised at what you learn from this exercise!
An Expert's Answer: Another physicist, claimed
that the Lorentz force must be used to solve this problem. That is not true.
The Lorentz force describes the effects on the electron moving in
magnetic field. In this case, we assume the charges to be moving in a straight
line in open space. The problem, as posed, does not therefore involve the
Lorentz force on the charges. Coulomb's law applies, and it is the most
reliable and thoroughly proven physics model in existence.
Suggestion: It is only necessary to consider
the one equipotential vertical line in the y-z plane in order
to see what is happening. All other lines in the y-z plane behave
similarly. The choice of using a straight line is to be able to see
changes in shape. You may be surprised at what you learn from this exercise!
It is extremely important due to the consequences presented by the shape
of the moving wave.
Recommendations: If you are sure you have
the answer, please let me know your
result, and we will comment on it. If you have trouble in finding the answer,
see what your scientific friends come up with and/or contact
me for an answer. Physics students may also want to pose this problem
to their professors. If needed, scroll down to the clue below:
Clue: The results of this exercise also correlate
to transverse (non-spherical) waves of electromagnetic radiation,
which move at the speed of light. Proven electromagnetic radiation
models have been in existence for at least 70 years. The model of electromagnetic
radiation can be graphed, and the shape of the waves in the far field produce
consistent patterns that have a certain resemblance to those of the above
moving dipole (see my paper on electromagnetic
radiation). If there is sufficient response to this puzzle, I will
expand this page in accordance with the responses. Send questions using