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Charges -q and +q at points A and B form a dipole with AB = 2a. O is the midpoint and OP is perpendicular to AB (equatorial line). A charge Q is at P with OP = y, where y >> 2a, and experiences force F. If Q is moved along the equatorial line to P' with OP' = y/3, what is the new force on Q (approximately)?

1. F/3
2. 3F
3. 9F
4. 27F

Correct answer: 27F

Solution

For y >> 2a, the equatorial field of a dipole is E = k*p/y³, so force F is proportional to 1/y³. Replacing y with y/3 multiplies the force by 3³ = 27. Hence the new force is 27F.

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