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Q.

Electric field in a space varies with x as E=(xi^+10j^) where x is in meter. Then the total charge contained within a prism as shown is xε0. The value of x is 

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answer is 6.

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Detailed Solution

Flux through area OPQ and area RST  is zero as field perpendicular to these areas is zero.

Flux entering through area OQRS is exiting through area PQRT.

Flux entering through area POST is also zero as the field perpendicular to the area POST is zero i.e, Ex=x Ex=0=0.

So, the net flux will exiting through area PQRT.

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At X=x consider a dx element 

dϕ= Ex.Area perpendicular to Ex=(x).2.23dx=4x3dx

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Therefore, ϕ=034x3dx=2x2303=6

ϕ=qε0=6

 q=6ε0

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