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Question

The volume charge density as a function of distance x from one face inside a unit cube is varying as shown in the figure. Then the total flux (in S.I. units) through the cube if (ρo=8.85×1012Cm3) is :


A
14
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B
12
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C
34
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D
1
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Solution

The correct option is C 34
Given A=1 m2
We know that,
dq=ρdV
dq=ρAdx
q=Aρdx
ρdx=Area under ρx curve
qenclosed=12(12+1)ρo
qenclosed=34ρo
So, total flux through the cube, ϕ=qenclosedϵo=3ρo4ϵo=34
(ϵo=8.85×1012)

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