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Question
Two equal point charges of the same sign are fixed on the y-axis, on either side of the origin equidistant from it, with the distance between them d. A third charge moves along the x-axis. The distance of the third charge from either of the two fixed charges when force on the third charge is maximum will be ______ cm.
[d = 10 cm]
Options
11.20
12.20
11.25
10.22
Solution
Two equal point charges of the same sign are fixed on the y-axis, on either side of the origin equidistant from it, with the distance between them d. A third charge moves along the x-axis. The distance of the third charge from either of the two fixed charges when the force on the third charge is maximum will be 12.20 cm.
Explanation:
`F_"net" = (2KQq)/((d^2 + x^2))[x/([d^2 + x^2]^{1"/"2})]`
`(dF_{Net})/dx = 0`
`x = d/sqrt2`
Required distance,
`sqrt(d^2 + d^2/2) = dsqrt3/2`
= 10 × 1.2
= 12.2 cm
