KVPY Sample Paper KVPY Stream-SX Model Paper-21

  • question_answer
    The conducting spheres of radii r and 3r initially have charges 3q & q respectively. Their separation is much larger than their radii. If they are joined by a conductor of high resistance, the force between them will -

    A) Increase continuously

    B) Decrease continuously

    C) First increase, then decrease

    D) First decrease, then increase

    Correct Answer: C

    Solution :

    Let charge on smaller sphere be x and on larger sphere be \[4q-x\]
    Force between them is given by
    \[\frac{dF}{dx}=0\Rightarrow 4q-2x=0\Rightarrow x=2q\]
    \[\therefore \]It represents a maximum.
    Final charges on the smaller sphere and the larger sphere are q & 3q respectively as required by the equality of potentials
    \[\therefore \]Force will increase until the charges becomes equal and after that force will decreases.

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