Challenging pendulum experiment
- In 1986 in a one-page paper "Electrostatic levitation of a dipole"
(Am. J. Phys. 54, 744, 1986) D. J. Griffiths showed that there is a
levitation force acting on a dipole at rest in a gravitational field.
The paper is available at:
The classical electromagnetic mass theory explains why this is
happening: the attraction between the dipole charges in a
gravitational field becomes unbalanced (due to the anisotropic
velocity of electromagnetic signals there) which gives rise to a
resultant electric self-force F directed against g:
F = - m'g
where m' is the electromagnetic mass that corresponds to the energy E
of the electric fields of the charges (m' = E/c^2). Unbalanced
repulsion of two like charges in a gravitational field leads to a
self-force F directed along g:
F = m'g.
For more on this explanation and a diagram of the electric fields and
forces acting on a dipole in a gravitational field see the
paper "Electric dipole in a gravitational field" and the other papers
The above effects can in principle be experimentally tested. If a
commercial capacitor is used as a pendulum bob the levitating self-
force F will lead to a longer period of the pendulum:
T = 2 pi (l/g)^1/2 [1 + (1/2)(m'/m)] (1)
where l is the length of the pendulum and m is its mass.
When the capacitor is not charged (m'=0) the period of the pendulum
is given by the standard expression:
T = 2 pi (l/g)^1/2
We are preparing to perform this experiment at Concordia University
in Montreal using a capacitor of 1F. We can determine the period with
an accuracy of 0.1 ms but we would prefer 0.01 ms.
If there are people interested in doing this experiment let me know
by sending me the data of the capacitor you intend to use: most
importantly - the total area of the metal foil and the distance
between the metal foils. Once I have this information I will
calculate the effect. You can also calculated it on the basis of what
is given in the paper mentioned above.
P. S. Several colleagues and I had the intention to try that
experiment some time ago. One of the reasons for the delay was my
mistaken conclusion at one point (due to doing several things at the
same time) that the described effect could not be tested with a
pendulum. Given the levitating force, everyone can derive eq. (1).