Two small spheres are charged positively, the combined charge being $5.0 \times 10^{- 5} C$ . If each sphere is repelled from the other by a force of $1.0 N$ when the spheres are $2.0$ metre apart, how is the total charge distributed between the spheres?

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Solution

Let the charge on one sphere be $q_{1}$ .
Charge on other sphere $q_{2} = 5 \times 10^{- 5} - q_{1}$
Force between them $F = \frac{K q_{1} q_{2}}{d^{2}}$
where $d = 2 m$
Or, $1 = \frac{9 \times 10^{9} \times q_{1} (5 \times 10^{- 5} - q_{1})}{2^{2}}$
$⟹ q_{1}^{2} - 5 \times 10^{- 5} q_{1} + 0.44 \times 10^{- 9} = 0$
We get $q_{1} = 1.15 \times 10^{- 5} C$
Charge on other sphere $q_{2} = (5 - 1.15) \times 10^{- 5} = 3.85 \times 10^{- 5} C$

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Two small spheres are charged positively, the combined charge being 5.0×10−5C. If each sphere is repelled from the other by a force of 1.0N when the spheres are 2.0 metre apart, how is the total charge distributed between the spheres?

Let the charge on one sphere be q1.Charge on other sphere q2=5×10−5−q1Force between them F=Kq1q2d2where d=2 mOr, 1=9×109×q1(5×10−5−q1)22⟹ q21−5×10−5q1+0.44×10−9=0We get q1=1.15×10−5 CCharge on other sphere q2=(5−1.15)×10−5=3.85×10−5 C

Two small spheres are charged positively, the combined charge being $5.0 \times 10^{- 5} C$ . If each sphere is repelled from the other by a force of $1.0 N$ when the spheres are $2.0$ metre apart, how is the total charge distributed between the spheres?