A) increase continuously
B) decrease continuously
C) first increase, then decrease
D) first decrease, then increase.
Correct Answer: C
Solution :
Let charge on smaller sphere be x and on larger sphere be \[4q-x\] force between them is given by \[F=\frac{k\,x\,(4q-x)}{{{d}^{2}}}\] |
\[\frac{dF}{dx}=0\]\[\Rightarrow \]\[4q-2x=0\]\[\Rightarrow \]\[x=2q\] |
\[\frac{{{d}^{2}}F}{d{{x}^{2}}}=\frac{K}{{{d}^{2}}}(-\,2)<0\] |
\[\therefore \] it represents a maximum. |
Final charges on the smaller sphere and the larger sphere are q & 3q respectively as required by the equality of potentials |
\[\therefore \] force will increase until the charges become equal and after that force will decrease. |
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