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Moving electroscope paradox?
Suppose you have two positively charged plastic spheres suspended from a common point by two strings. The balls will repel each other, and the strings will form a certain angle with the vertical, which depends on the balls' weight, the amount of charge, and the length of the string.
But now suppose you take this device on a train, which is moving perpendicular to the line joining the two balls. From the point of view of a stationary observer, the moving charges now form two parallel electrical currents. (To make this easier to picture as a "current", imagine the train contains hundreds of identical such devices, space at 1-foot intervals along the length of the train.)
Now, we all know that parallel currents create an attractive magnetic force--This is why two wires containing parallel currents will attract each other. This means the repulsive electrical force holding the balls apart, should be slightly mitigated by the attractive magnetic force; and this means the balls' separation should be reduced somewhat.
But from the point of view of a passenger on the train, the charges are NOT moving, so there is no magnetic force, and the ball's separation should NOT be reduced.
So, which of these two possibilities actually happens?
Here's my guess: The separation is actually reduced. The stationary observer explains this in terms of magnetic attraction. The train passenger explains it in terms of an increased gravitational force on the balls. Because of relativistic length contraction, the (relatively moving!) mass of the earth under the train increases in density, thus exerting a stronger downward force on the balls than a "stationary" earth.
2 Answers
- ?Lv 77 years agoFavorite Answer
Hi Rick - great question. My guess - the separation is not affected.
The passenger on the train sees no difference in behaviour - the charges are not moving. Nor is the mass of the earth moving- the train maintains a (relatively) constant distance from its centre of mass.
The balls are perpendicular to the direction of travel so there is no Lorentz contraction -either in the space of the balls or the ruler used to measure.
Still thinking about the stationary observer.
- OldPilotLv 77 years ago
Both.
Space diliation will make it appear to the motionless observer that the balls move closer together.
The observer on the train is not aware of the diliation and to that observer the balls do not move
Source(s): EDIT: For the balls perpendicular to the direction of motion, the 2 balls are motionless with respect to that Frame of Reference ====> No magnetic field generated with respect to that FoR.