Two spherical conductor $B$ and $C$ having equal radii and carrying equal charges in them repel each other…

Two spherical conductor $B$ and $C$ having equal radii and carrying equal charges in them repel each other with a force $F$ when kept apart at some distance. A third spherical conductor having same radius as that of $B$ but uncharged brought in contact with $B$, then brought in contact with $\mathrm{C}$ and finally removed away from both. The new force of repulsion, between $B$ and $C$ is
  1. $\mathrm{F} / 4$
  2. $3 F / 4$
  3. $\mathrm{F} / 8$
  4. $3 \mathrm{~F} / 8$.

Solution

$F^{\prime}=\frac{1}{4 \pi \varepsilon_0} \frac{(q / 2)(3 q / 4)}{d^2}=\frac{3 F}{8}$

Asked in: JEE Main 2004

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