Physics, 11.02.2022 02:10 queengenni
A charge is divided q1 and (q-q1)what will be the ratio of q/q1 so that force between the two parts placed at a given distance is maximum?
Answers: 1
, assuming that 
and 
are point charges.
denote the coulomb constant. Let 
denote the distance between the two point charges. In this question, neither 
.
with respect to 
.)![\begin{aligned}\frac{d}{d q_{1}}[F] &= \frac{d}{d q_{1}} \left[\frac{k}{r^{2}}\, (q\, q_{1} - {q_{1}}^{2})\right] \\ &= \frac{k}{r^{2}}\, \left[\frac{d}{d q_{1}} [q\, q_{1}] - \frac{d}{d q_{1}}[{q_{1}}^{2}]\right]\\ &= \frac{k}{r^{2}}\, (q - 2\, q_{1})\end{aligned}](/tpl/images/2653/4708/1d6db.png)
.![\begin{aligned}\frac{d^{2}}{{d q_{1}}^{2}}[F] &= \frac{d}{d q_{1}} \left[\frac{k}{r^{2}}\, (q - 2\, q_{1})\right] \\ &= \frac{(-2)\, k}{r^{2}}\end{aligned}](/tpl/images/2653/4708/52359.png)
.
. Thus, the value of the second derivative of 
would be convex over all 
with respect to 
, there would be a unique 
should be 
. In other words:
.
.
.
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A charge is divided q1 and (q-q1)what will be the ratio of q/q1 so that force between the two parts...
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