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Question

Eight charges 1 μC,7 μC,4 μC,10 μC, 2 μC,5 μC,3 μC and 6 μC are situated at the eight corners of a cube of side 20 cm. A spherical surface of radius 80 cm encloses this cube. The centre of the sphere coincides with the centre of the cube. Then, the total outgoing flux from the spherical surface (in units of V-m) is,

A
36π×103
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B
684π×103
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C
Zero
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D
81π×103
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Solution

The correct option is C Zero
The spherical surface encloses the cube hence the total charge enclosed by the sphere is,
qencl=1 μC+(7 μC)+(4 μC)+10 μC+2 μC+(5 μC)+(3 μC)+6 μC

qencl=0

Applying Gauss's law to the spherical surface,

ϕtotal=qenclϵ0

ϕtotal=0

Hence, (C) is the correct answer.

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