- #1
kamil9876
- 6
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Ok for the record I havn't studied physics in a year, I'm a math student. But I was reminded of a paradox I came up with once in physics:
Suppose we place a positively charged ball above an infinite plane with positive charge. We know by Gauss law that the electric force on the ball ends up being constant and independent of the height. Suppose that the gravitation force pulling it down is stronger than the repulsion force. Hence the ball falls with constant acceleration all the way.
Now if I was to remove every point in this plane except for the one just below the ball, then clearly the repulsion force is weaker and hence the ball should continue moving. But using the q1q2/r^2 formula we see that the force should eventually become stronger than gravity and so it shouldn't fall down all the way.
?
Back then I resolved this by saying that, "oh a point has zero area hence the charge is 0 hence it falls all the way(if it had some non-zero charge then, assuming uniformity, any subset of the plane with non-zero area would have infinite charge". But still, what if it was just an proton or something like that?
Suppose we place a positively charged ball above an infinite plane with positive charge. We know by Gauss law that the electric force on the ball ends up being constant and independent of the height. Suppose that the gravitation force pulling it down is stronger than the repulsion force. Hence the ball falls with constant acceleration all the way.
Now if I was to remove every point in this plane except for the one just below the ball, then clearly the repulsion force is weaker and hence the ball should continue moving. But using the q1q2/r^2 formula we see that the force should eventually become stronger than gravity and so it shouldn't fall down all the way.
?
Back then I resolved this by saying that, "oh a point has zero area hence the charge is 0 hence it falls all the way(if it had some non-zero charge then, assuming uniformity, any subset of the plane with non-zero area would have infinite charge". But still, what if it was just an proton or something like that?