બે એકસમાન વાહક ગોળા A અને B પર સમાન વિજભ | vedclass

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Question

Spheres $A$ and $B$ carry equal charge say $'q$

$	herefore $ Force between them, $\mathrm{F}=\frac{\mathrm{k} \mathrm{qq}}{\mathrm{r}^{2}}$

Vedclass · Accepted Answer

$\frac{{3F}}{8}$

Vedclass · Answer

Spheres $A$ and $B$ carry equal charge say $'q$

$	herefore $ Force between them, $\mathrm{F}=\frac{\mathrm{k} \mathrm{qq}}{\mathrm{r}^{2}}$

When $A$ and $C$ are touched, charge on both

$\mathrm{q}_{\mathrm{A}}=\mathrm{q}_{\mathrm{C}}=\frac{\mathrm{q}}{2}$

Then when $\mathrm{B}$ and $\mathrm{C}$ are touched, charge or $B$

$\mathrm{q}_{\mathrm{B}}=\frac{\frac{\mathrm{q}}{2}+\mathrm{q}}{2}=\frac{3 \mathrm{q}}{4}$

Now, the force between charge $q_{A}$ and $q_{B}$

$\mathrm{F}^{\prime}=\frac{\mathrm{k} \mathrm{q}_{\mathrm{A}} \mathrm{q}_{\mathrm{B}}}{\mathrm{r}^{2}}=\frac{\mathrm{k} 	imes \frac{\mathrm{q}}{2} 	imes \frac{3 \mathrm{q}}{4}}{\mathrm{r}^{2}}=\frac{3 \mathrm{kq}^{2}}{8} \mathrm{r}^{2}=\frac{3}{8}\, \mathrm{F}$

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