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Question

A non-conducting sphere of radius 0.5 m carries a total charge of 10×1010 C distributed uniformly which produces an electric field. Then the value of integral
0Edr will be

A
9
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B
27
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C
0
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D
27
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Solution

The correct option is B 27
Given that,
Radius of the sphere, R=0.5 m
Charge of the sphere, Q=10×1010 C

The given integral represent the relation between electric field and electric potential.
0Edr = Potential at centre of sphere - Potential at infinity

The potential at infinity is zero
V = 0
The potential at the centre of the sphere is
Vcentre=3kQ2R
Vcentre=3×9×109×10×10102×0.5=27

So 0Edr=27

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