The total charge enclosed in an incremental volume 2 10^-9m^3 of located at the origin is ____ nC, if electric flux density of its field is found as D=e^-x sinyi-e^-x cosyj+2zkC/m^2.

Question

Accepted Answer

Correct answer: 4. (4) Electric flux density (D )= ch arge Area r= Q4 r^2r= ∈_0 ( Q4 ∈_0r^2r ) ⇒E= D ∈_0= e^-x sinyi-e^-x cosy+2zk ∈_0 Also by Gauss's law ∈_0=( ∂ ∂xi+ ∂ ∂yj+ ∂ ∂zk) .E=( ∂ ∂xi+ ∂ ∂yj+ ∂ ∂zk) . D ∈_0 ⇒ = ∂ ∂x (e^-x siny )+ ∂ ∂y(-e^-x cosy)+ ∂ ∂x (2z ) At origin =-e^-0 sin0+e^-0 sin0+2 =2C/m^3 Charge = volume =2 2 10^-9=4 10^-9=4 nC

$The total charge enclosed in an incremental volume 2 \times 1 0^{- 9} m^{3} of located at the origin is ____ nC, if electric flux density of its field is found as D = e^{- x} sin y i - e^{- x} cos y j + 2 z k C / m^{2} .$

Solution

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