Question

Three point charges ` Q, 4 Q` and ` 16 Q` are placed on a straight line ` 9 cm` long. Charges are placed in such a wat that the system has minimum potential energy . Then .
A. `4Q` and `16 Q` must be at the ends and `Q` at a distance of `3` cm from the `16Q`
B. `4Q` and `16 Q` must be at the ends and `Q` at a distance of `3` cm from the `16Q`
C. Electric field at the position of `Q` at a distance of `6 cm` from the `16 Q`.
D. Electric field at the position of `Q` at a distance of `6 cm` from the `16 Q`.

Answer 1

Correct Answer - B::C
For potential enrgy to be minmuum charge ` 11 Q` and ` 16Q` to be placed at the ebd of line
` U = (Kq_1q_2)/r_(12) + (Kq_1q_3)/r_(13) + (Kq_2q_3)/r_(23)`
`U= (K. 4Q.Q)/((9-x) xx 10^(-12)) + (K. (4 Q) 16Q)/((9) xx 10^(-2)) + (KQ.16Q)/x`
` U= 4/((9-x)) + 100KA^2 . (64)/9 + 100 KQ^2`
for `U` to be minimum `(dU)/(dx) =0`
`1/((9-0x)^2) = 4/x^2`
`(0-x)^2 x^2`
` x= 6 cm or 18 cm`
since ` F=- (dU)/(dx) rArr F0.`, when `U` is min.