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Two isolated sphereical conductors have radii {5}{c}{m} and {0

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Two isolated sphereical conductors have radii $5 c m$ and $0 c m$ , espctively They have charges of $12 μ C$ and $- 3 μ C$ . Find the charges after they are connected by a conductng wire. Also find the common potential after resistribution.

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Two isolated sphereical conductors have radii

5 c m

and

0 c m

, espctively They have charges of

12 μ C

and

- 3 μ C

. Find the charges after they are connected by a conductng wire. Also find the common potential after resistribution.

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Text solutionVerified

Solution:

net charge

= (12 - 3) μ C = 9 μ C

Charge is distributed in the ratio of their capacities (or radii in case of spherical conductors), i.e.

\frac{q _{1}^{^{'}}}{q _{2}^{^{'}}} = \frac{R _{1}}{R _{2}} = \frac{5}{10} = \frac{1}{2}

q_{1}^{^{'}} = (\frac{1}{1 + 2}) (9) = 3 μ C

and q_{2}^{^{'}} = (\frac{2}{1 + 2}) (9) = 6 μ C

conmon potential

V = \frac{q _{1} + q _{2}}{C _{1} + C _{2}} = (\frac{9 \times 10 ^{- 6}}{4 π ϵ _{0} ( R _{1} + R _{2} )}

\frac{( 9 \times 10 ^{- 6} ) ( 9 \times 10 ^{9} )}{( 15 \times 10 ^{- 2} )}

= 5.4 \times 10^{5} V

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Question Text	Two isolated sphereical conductors have radii $5 c m$ and $0 c m$ , espctively They have charges of $12 μ C$ and $- 3 μ C$ . Find the charges after they are connected by a conductng wire. Also find the common potential after resistribution.
Answer Type	Text solution:1
Upvotes	150