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Two diagrams each show a pair of infinitely long stationary line charges, both with the same positive linear charge density lambda, held parallel to one another. Point charges +q and -q are placed in equilibrium somewhere between them, free to move only along the x-direction. If each is displaced slightly from its equilibrium position, which statement(s) is/are correct?
- Both charges perform simple harmonic motion.
- Both charges keep moving in the direction they were displaced.
- +q performs SHM while -q keeps moving away in the displacement direction.
- -q performs SHM while +q keeps moving away in the displacement direction.
Correct answer: +q performs SHM while -q keeps moving away in the displacement direction.
Solution
Midway between two equal positive line charges the field cancels (equilibrium). Moving toward one line increases its (repulsive, for +q) field and decreases the other's, producing a net field pointing back toward center. For +q the force is opposite to displacement -> restoring -> SHM. For -q the force on it is opposite that on +q, hence along the displacement -> it is pushed further away (unstable). So +q oscillates (SHM) and -q runs away.
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