Question

Four closed surfaces, S1 through S4, together with the charges -2Q, Q, and -Q are sketched in the figure below. (The colored lines are the intersections of the surfaces with the page.) Find the electric flux through each surface. (Use the following as necessary: and Q.) Ss 0-e S1 S2 53 S4

Answer 1

Apply Gauss theorem in each closed surface to get Electric flux $\phi$ .

Gauss theorem states the Electric flux through a closed surface is equal to 1/ $\varepsilon$ _o times the total charged enclosed to the Gaussian surface.

Part 1

Let us take Gaussian surface S_{​​​​​​1}

Charged enclosed in it = (- 2 Q + Q)

= - Q

Apply Gauss theorem

$\phi$ _{s1= total charge / $\varepsilon$ o}

_{$\phi$ s1 = - Q / $\varepsilon$ o}

_{Part 2}

_{Total charge enclosed in surface S​​​​​}​​​​​​_{​​​​​​2= (+Q) + (- Q) = 0}

_{$\phi$ s2= total charge enclosed / $\varepsilon$ o}

_{$\phi$ s2 = 0}

Part 3

Total charge enclosed in surface S3

= ( -2Q) + (+Q) +(- Q)

= -2Q

$\phi$ _{s3 = total charge enclosed/ $\varepsilon$ o}

_{$\phi$ s3 = -2Q/ $\varepsilon$ o}

Part 4

Total charge enclosed in surafce S4 = 0

$\phi$ _{s4= total charge elclosed / $\varepsilon$ o}

_{$\phi$ s4 = 0}