Problem 13.11

จาก \(\vec{F}_{3} = \vec{F}_{13} + \vec{F}_{23}\)

r̂r̂

\(\vec{F}_{3} =\frac{kq_{1}q_{3}}{r_{13}^{2}}_{13} +\frac{kq_{2}q_{3}}{r_{23}^{2}}_{23}\)

îî

\(0 =\frac{k(q)(-q)}{x^{2}}+\frac{k(2.5q)(-q)}{(\ell  - x)^{2}}(- )\)

\(2.5x^{2} = (\ell - x)^{2}\)

\(2.5x^{2} = \ell ^{2} - 2\ell x + x^{2}\)

\(1.5x^{2} + 2\ell x - \ell ^{2} = 0\)

\(x =\frac{-2\ell \pm (2\ell )^{2}-4(1.5)(-\ell ^{2})}{2(1.5)}\)

\(x = 0.387\ell , -1.72\ell\)

\(\therefore x = 0.387\ell \;\blacksquare\)