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  • Two metal spheres, one of radius R and the other of radius 2R, both have the same surface charge density sigma. They are brought in contact and separated. What will be the new surface charge densities on them?

Two metal spheres, one of radius R and the other of radius 2R, both have the same surface charge density \sigma. They are brought in contact and separated. What will be the new surface charge densities on them?

Answers (1)

Let us say, the charge stored on the first and second metal spheres before contact is Q_{1} and Q_{2}  respectively.

Therefore,

Q_{1}=\sigma .4\pi R^2

Q_{2}=\sigma .4\pi (2R)^2=4\; Q_{1}

Again assume, the charge stored on the first and second metal spheres are Q{_{1}}^{'} and Q{_{2}}^{'} respectively.

Therefore,

\left ( Q{_{1}}^{'}+Q{_{2}}^{'} \right )=\left ( Q{_{1}}+Q{_{2}} \right )=5\; Q_{1}

When the metal spheres are in contact, the following is the potentials acquired by them

Q{_{1}}^{'} = \frac{Q{_{2}}^{'}}{2}

By solving the above equations, we get,

\sigma 1=5\frac{\sigma }{3}

\sigma 2=5\frac{\sigma }{6}

Posted by

infoexpert23

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