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=8.85×10–12Cm3) 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 C34 Given A=1m2
We know that, dq=ρdV ∫dq=∫ρAdx q=A∫ρdx ∫ρdx=Area under ρ−x curve ∴qenclosed=12(12+1)ρo ⇒qenclosed=34ρo
So, total flux through the cube, ϕ=qenclosedϵo=3ρo4ϵo=34 (∵ϵo=8.85×10−12)