The three small spheres shown in the figure (Figur...

Question

The three small spheres shown in the figure (Figure 1) carry charges q₁ = 3.95 nC, q₂ = -7.75 nC, and q₃ = 2.50 nC.

A. Find the net electric flux through the closed surface S₂ shown in cross section in the figure.

B. Find the net electric flux through the closed surface S₃ shown in cross section in the figure.

C. Find the net electric flux through the closed surface S₄ shown in cross section in the figure.

D. Find the net electric flux through the closed surface S₅ shown in cross section in the figure.

Patrick Ford · Accepted Answer

Electric flux is given by:ϕE=qenclε0[readmore]A.The charge enclosed in surface S2 is q2.Now we have:ϕ2=q2ε0=-7.75×10-98.85×10-12ϕ2 = - 875.71 Nm2/CThe net electric flux through the closed surface S2  is - 875.71 Nm2/C.B.The surface, S3 encloses charges q1 and q2.Therefore, the net electric flux is:ϕ3=(q1+q2)ε0=(3.95-7.75)×10-98.85×10-12ϕ3 = - 429.38 Nm2/CThe net electric flux through the closed surface S3 is - 429.38 Nm2/C.C.Surface S4 encloses charges q1 and q3.Thus:ϕ4=q1+q3ε0=(3.95+2.50)×10-98.85×10-12ϕ4 = 728.81 Nm2/CThe net electric flux through the closed surface S4 is 728.81 Nm2/C. D.Surface, S5 encloses charges q1, q2, and q4:Therefore:ϕ5=q1+q2+q3ε0=(3.95-7.75+2.50)×10-98.85×10-12ϕ5 = - 146.89 Nm2/CThe net electric flux through the closed surface S5 is - 146.89 Nm2/C.

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