Two identical metallic spheres A and B when placed at certain dis… - Vidyadip

MCQ

Two identical metallic spheres $A$ and $B$ when placed at certain distance in air repel each other with a force of $F$. Another identical uncharged sphere $C$ is first placed in contact with $A$ and then in contact with $B$ and finally placed at midpoint between spheres $A$ and $B$. The force experienced by sphere $C$ will be.

A
$3\,F / 2$
✓
$3\,F / 4$
C
$F$
D
$2\,F$

✓

Answer

Correct option: B.

$3\,F / 4$

b
Let $q _{ A }= q _{ B }= q$

When $C$ is placed in contact with $A$, charge on $A$ and $ C$ will be $=\frac{ q }{2}$

Now $C$ is placed in contact with $B$, charge on $B$ and $C$ will be $=\frac{q+\frac{q}{2}}{2}=\frac{3 q}{4}$

$F ^{\prime}= F _{2}- F _{1}=\frac{\left( K \frac{3 q }{4}- K \frac{ q }{2}\right)}{\frac{ r ^{2}}{4}} \cdot \frac{3 q }{4}$

$=\frac{3 Kq ^{2}}{4 r ^{2}}=\frac{3 F }{4}$

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