Two spherical conductors B and C having equal radii and carrying … - Vidyadip

MCQ

Two spherical conductors $B$ 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 is brought in contact with $B$, then brought in contact with $C$ and finally removed away from both. The new force of repulsion between $B$ and $C$ is

A
$F/4$
B
$3F/4$
C
$F/8$
✓
$3F/8$

✓

Answer

Correct option: D.

$3F/8$

d
(d) Initially $F = k.\frac{{{Q^2}}}{{{r^2}}}$ (fig. $A$). Finally when a third spherical conductor comes in contact alternately with $B$ and $C$ then removed, so charges on $B$ and $C$ are $Q / 2$ and $3Q / 4$ respectively (fig. $B$)

Now force $F' = k.\frac{{\left( {\frac{Q}{2}} \right)\,\left( {\frac{{3Q}}{4}} \right)}}{{{r^2}}} = \frac{3}{8}F$

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