Problem #1
Four closed surfaces, S1 through S4, together with the charges -2Q , +Q , and -Q are sketched in Figure . (The colored lines are the intersections of the surfaces with the page.) Find the electric flux through each surface.
the electric flux through each surface is
ΦE = Qin/ϵ0
(Through S1) ΦE = (–2Q + Q)/ϵ0 = –Q/ϵ0
(Through S2) ΦE = (Q – Q)/ϵ0 = 0
(Through S3) ΦE = (–2Q + Q – Q)/ϵ0 = –2Q/ϵ0
(Through S4) ΦE = 0
Problem #2
A charge of 170 μC is at the center of a cube of edge 80.0 cm. (a) Find the total flux through each face of the cube. (b) Find the flux through the whole surface of the cube.
Answer:
Known:
charge of Q = 170 μC = 170 x 10-6 C
ΦE = Qin/ϵ0 = 170 x 10-6 C/8.85 x 10-12 C2/N.m2 = 1.92 x 107 N.m2/C2
(a) the total flux through each face of the cube is
(ΦE)one-face = ΦE/6 = 1.92 x 107 N.m2/C2/6 = 3.20 x 106 N.m2/C2
(b) the flux through the whole surface of the cube is 1.92 x 107 N.m2/C2
Problem #3
Determine the electric flux for a Gaussian surface that contains 200 million electrons.
Answer:
the electric flux through each surface is
ΦE = Qin/ϵ0 = 200 x 106 (1.6 x 10-19)/8.85 x 10-12 = 3.6 N.m2/C
Problem #4
The following charges are located inside a submarine: 5.00 μ C, -9.00 μ C, 27.0 μ C, and -84.0 μ C. (a) Calculate the net electric flux through the hull of the submarine. (b) Is the number of electric field lines leaving the submarine greater than, equal to, or less than the number entering it?
Answer
(a) the net electric flux through the hull of the submarine is
ΦE = Qin/ϵ0 = (+5.00 µC – 9.00 µC + 27.0 µC – 84.0 µC)/(8.85 x 10-12 C2/N.m2)
ΦE = –6.89 x 106 N.m2/C2
(b) Since the net electric flux is negative, more lines enter than leave the surface
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