A charged sphere of radius $0.02 m$ has charge density of $1 {Cm}^{- 2}$ . The workdone when a charge of $40 nC$ is moved from infinity to a point that is at a distance of $0.04 m$ from the centre of the sphere.

1.44 π J

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2 J

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14.4 π J

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1.44 J

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Solution

The correct option is C $14.4 π J$
Charge on sphere is
$Q = σ S = σ \times 4 π r^{2} = 1 \times 4 π \times (0.02)^{2}$

$= 4 π \times 4 \times 10^{- 4} = 16 π \times 10^{- 4} C$

Workdone $=$ P.E. of the system of two charges

$W = \frac{1}{4 π ε_{0}} \frac{Q q}{r}$

$= \frac{9 \times 10^{9} \times 16 π \times 10^{- 4} \times 40 \times 10^{- 9}}{0.04}$

$= 9 \times 16 π \times 10^{- 1}$

$= 14.4 π J$

 Hence, (c) is the correct answer.

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A charged sphere of radius 0.02 m has charge density of 1 Cm−2. The workdone when a charge of 40 nC is moved from infinity to a point that is at a distance of 0.04 m from the centre of the sphere.

A charged sphere of radius $0.02 m$ has charge density of $1 {Cm}^{- 2}$ . The workdone when a charge of $40 nC$ is moved from infinity to a point that is at a distance of $0.04 m$ from the centre of the sphere.