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  4. Two identical spheres with charges 4q,-2q kept some distance apart exert a force F on each other. If they are made to touch each other and replaced at their old positions, the force between them will be

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Q. Two identical spheres with charges $ 4q,-2q $ kept some distance apart exert a force $F$ on each other. If they are made to touch each other and replaced at their old positions, the force between them will be

J & K CETJ & K CET 2006Electric Charges and Fields

Solution:

When spheres are touched and separated, charge is
$q'=\frac{4 q-2 q}{2}=\frac{2 q}{2}=q$
From Coulomb's law
$F =\frac{1}{4 \pi \varepsilon_{0}} \frac{(4 q)(-2 q)}{r}$...(i)
When made to touch
$F '=\frac{1}{4 \pi \varepsilon_{0}} \frac{q^{2}}{r}$ ...(ii)
From Eqs. (i) and (ii), we get
$F'=\frac{F}{8}$