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Electric Potential and Potential Difference

Two conductin...

Question

Two conducting spheres of radii $R_{1}$ and $R_{2}$ and changed with charges $Q_{1}$ and $Q_{2}$ respectively. On bringing them in contact there is:

No change in the energy of the system

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An increase in the energy of the system if

Q_{1} R_{2} \neq Q_{2} R_{1}

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Always a decrease in energy of the system

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A decrease in energy of the system if

Q_{1} R_{2} \neq Q_{2} R_{1}

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Solution

The correct option is D A decrease in energy of the system if $Q_{1} R_{2} \neq Q_{2} R_{1}$
In contact $V_{1} = V_{2}$
$\frac{Q_{1}}{R_{1}} = \frac{Q_{2}}{R_{2}}$
But if $\frac{Q_{1}}{R_{1}} \neq \frac{Q_{2}}{R_{2}}$
$Q_{1} R_{2} \neq Q_{2} R_{1}$
E is always decreasing if $Q_{1} R_{2} \neq Q_{2} R_{1}$

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