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Principle of Superposition

Two equally c...

Question

Two equally charged identical metal spheres A and B repel each other with a force F. Another identical uncharged sphere C is touched to A and then placed midway between A and B. The net force on C is in the direction:

A

F

towards A

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B

F

towards B

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C

2 F

towards A

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D

2 F

towards B

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Solution

The correct option is A $F$ towards A
The spheres are equally charged. Let the charge be $q$ .
Now, using coulombs law,
$k q^{2} / r^{2} = F$ ( $r$ is the distance between the two spheres )
When the uncharged sphere touches A, $q / 2$ charge gets transferred to C
Now, force on C,
$= \frac{k (q / 2) (q / 2)}{(r / 2)^{2}} - \frac{k (q / 2) (q)}{(r / 2)^{2}} = k q^{2} / r^{2} - 2 k q^{2} / r^{2} = - F$
Net force is thus towards A.

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