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: ε0 and Q.) Three charges are aligned vertically where the top charge is −2Q, the middle charge is +Q, and the bottom charge is −Q. Four loops of arbitrary shape are drawn, each enclosing a different set of charges. S1 is red and contains the top two charges. S2 is blue and contains the bottom two charges. S3 is black and contains all three charges. S4 is green does not contain any charges. ΦS1 = ΦS2 = ΦS3 = ΦS4 =

Answer 1

Gauss's Law: Electric flux through the gaussian surface is $\phi_E=\frac{q_{enclosed}}{\epsilon_0}$

The surface $S_1$ encloses  two charges $-2Q,+Q$ , electric flux $\phi_S_1=\frac{-2Q+Q}{\epsilon_0}=\frac{-Q}{\epsilon_0}$

The surface $S_2$ encloses  two charges $+Q,-Q$ , electric flux $\phi_S_2=\frac{+Q-Q}{\epsilon_0}=0$

The surface $S_3$ encloses  three charges $-2Q,+Q,-Q$ , electric flux $\phi_S_3=\frac{-2Q+Q-Q}{\epsilon_0}=\frac{-2Q}{\epsilon_0}$

The surface $S_4$ encloses  no charges   , electric flux $\phi_S_4=\frac{0}{\epsilon_0}=0$