The electric potential in a medium of dielectric constant ‘unity’ is ϕ(x,y,z)=ax2 where ‘a’ is a constant of suitable dimensions. The total charge contained in a cube of dimensions −L≤x,y,z≤L is

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zero

−2a∈0L3

−16a∈0L3

−4a∈0L3

answer is D.

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Detailed Solution

ϕ(x,y,z)=ax2 E→=−2axi^∫B E→⋅ds→=(2aLi^)L2i^=2aL3∫Bx=−L E→ds→=(−2a(L)i^]⋅L2i^=−2aL3∫ E→ds=0 (for all other faces)∴∮ E→⋅ds→=−4aL3=qϵ0∴q=−4a∈0L3

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