Question

Two identical metallic spheres A and B each carrying a charge q repel each other with force F a third metallic uncharged sphere C of same size is made to touch the spheres A and B alternately and the moved away what is the force of repulsion between A and B

Answer 1

Answer:

The force of repulsion between the spheres is $\frac{3Kq^2}{8d^2}$.

Explanation:

The initial force between both the spheres is given as,

$F=\frac{Kq^2}{r^2}$     (1)

Where,

F=force between the spheres

K=coulombs constant

q=charge on the individual spheres

• When sphere C comes into contact with sphere A, both spheres' final charges become,

                                      $q'=\frac{q}{2}$      (2)

• When this sphere C comes into contact with sphere B, the ultimate charges on both of them will be given as,

                            $q''=\frac{\frac{q}{2} +q}{2} =\frac{3q}{4}$      (3)

The new force of repulsion between A and B is given as,

$F'=\frac{K\times \frac{q}{2}\times \frac{3q}{4} }{r^2}$      

$F'=\frac{3Kq^2}{8d^2}$      (4)

By comparing equations (1) and (4) we get;

$F'=\frac{3F}{8}$        

Hence, the force of repulsion between the spheres is $\frac{3Kq^2}{8d^2}$.

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