1. Measuring Propagation Speed of Coulomb Fields
R. de Sangro, G. Finocchiaro, P.Patteri,
M. Piccolo, G. Pizzella
Eur. Phys. J. C (2015)

2. 1920

5. The force attracting the Earth to the Sun is directed to a point where the Sun actually is, not to the point where we see it We study now the problem in electromagnetism, where a similar situation occurs

6. Retarded potentials in electromagnetism

8. electrical charge with constant velocity

10. Let us calculate the electric field expected when using the L-W formula

11. Measuring Emax
Detector
At y=30 cm at
g=1000

12. The experiment at BTF (measurements made from 2009 thru 2014) beam length L = 3 m

15. Normalized amplitudes Sn for sensors A1(upper) and A3(lower) for A5;A6 =172.0 cm. The continuous line at mV (upper) and mV (lower) indicate the weighted average of our measurements. The six measurements plotted refers to the transverse positions of A5, A6. The dashed line:

16. As previous figure for A5;A6= 329.5 cm.

17. As previous figure for A5;A6= 552 cm.

18. Upper graph: the ratio Vmax(A5)/Vmax(A1) at A5;A6=172
Upper graph: the ratio Vmax(A5)/Vmax(A1) at A5;A6=172.0 cm versus the transverse distance. Lower graph: Vmax(A6)/Vmax(A3) . The continuous lines are the theoretical ones

19. The same plot as in previous figure at A5;A6=329.5 cm

20. The same plot as in previous figure at A5;A6=552 cm

21. In spite of the very good agreement between measurements and calculations, we want to make sure that we do measure the Coulomb field and not measure electromagnetic radiation.
We put a lead block between the reference sensors A1,A2,A3,A4 and the movable sensors A5, A6, in order to stop the beam and forbid it to go under the sensors A5,A6.

23. The result

24. The result

25. conclusion
Assuming that the electric field of the electron beams act on our sensor only after the beam itself has exited the beam pipe, the L.W model predicts sensors responses orders of magnitudes smaller than what we measure. The Feynman interpretation of the Lienard-Weichert formula for uniformly moving charges does not show consistency with our experimental data. Even if the steady state charge motion in our experiment lasted few tens of nanoseconds, our measurements indicate that everything behaves as if this state lasted for much longer.

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