Define electric flux and write its SI unit . The electric field components in the figure shown are : `E_(x)=alphax,E_(y)=0,E_(z)=0` where `alpha=(100N)/(Cm)`.
Calculate the charge within the cube , assuming a = 0.1 m .

Explanation

Electric flux : Number of electric field lines passing through a given area normally is called electric flux . It is a scalar quantity . It is denoted by `phi_(E)`.
`phi_(E)=int vecE.vec ds` where E is electric fields intensity and ds is area element. Its SI unit is `Nm^(2)c^(-1)`.
Given : a = 0.1 M
`Ex=alphax` " " `alpha=(100N)/(Cm)`
Ey = 0
Ez = 0
Electric flux associated with surface ABCE
`phi_(1)=vecE_(x).vecS=E_(x)Scos180^(@)=(alpha a)(a^(2))(-1)=-alpha a^(3)`.
Electric flux associated with surface EFGH
`phi_(2)=vecE_(x).vecS=E_(x)Scos0^(@)=alpha(2a)(a^(2))(1)=2alphaa^(3)`.
Net flux associated with the cube `phi=phi_(1)+phi_(2)`
`phi=-alpha a^(3)+2alphaa^(3)=alpha a^(3)=100 xx0.1xx0.1xx0.1=0.1NM^(2)C^(-1)`
According to Gauss theorem
`q=in_(0)phi=8.85xx10^(-12)xx0.1=8.85xx10^(-13)C`.