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Charge Behaviour

A metal spher...

Question

A metal sphere A of radius $r_{1}$ charged to a potential $ϕ_{1}$ is enveloped by a thin walled conducting spherical shell B of radius $r_{2}$ . Then potential $ϕ_{2}$ of the sphere A after it is connected to the shell B by a thin conducting wire will be :-

ϕ_{1} \frac{r_{1}}{r_{2}}

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ϕ_{1} (\frac{r_{2}}{r_{1}})

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ϕ_{1} (1 - \frac{r_{2}}{r_{1}})

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ϕ_{1} (\frac{{r_{1} r}_{2}}{r_{1} + r_{2}})

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Solution

The correct option is A $ϕ_{1} \frac{r_{1}}{r_{2}}$
The charge $q_{1}$ can be obtained form
$q_{1} = u π ϵ_{0} ϕ_{1} r_{1}$
After the connection the entire charge $q_{1}$ will
How form the sphere to the enveloped and
will be distributed uniformly overs its surface
$ϕ_{2} = \frac{q_{1}}{u π ϵ_{0} r_{2}} = ϕ_{1} \frac{r_{1}}{r_{2}}$

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A metal sphere A of radius r1 charged to a potential ϕ1 is enveloped by a thin walled conducting spherical shell B of radius r2. Then potential ϕ2 of the sphere A after it is connected to the shell B by a thin conducting wire will be :-

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