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Identical point charges are placed at all vertices of a cube of edge length a. Each charge experiences a net force of magnitude F. The same set of charges is then placed at the vertices of another cube of edge length b. What is the magnitude of the net force on any one of the charges in the second arrangement?
- aF/b
- bF/a
- a²F/b²
- b²F/a²
Correct answer: a²F/b²
Solution
When the cube edge changes from a to b, all inter-charge distances scale by b/a. Since Coulomb force is proportional to 1/r², each component force scales by (a/b)², and so does the net force.
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