(5%) Problem 5: A combination of four charges and four Gaussian surfaces are dis

Question

(5%) Problem 5: A combination of four charges and four Gaussian surfaces are displayed in the figure. The charges have values gi 7 C, g2 C, g3 16 nC, and q4 17 nC A 25% Part (a) t is the flux through the first surface, Si, in N C? HOME Cosi 4 5 6 cotan 1 2 3 atan acotan cosh0 tanh0 cotanh0 o Degrees O Radians Submit Hint I give up Feedback 006 deduction per feedback. Hints 1% deduction per hint. Hints re maining A 25% Part (b) What is the flux through the second surface, S2, in Nm C? A 25% Part (c) What is the flux through the third surface, S3, in Ni C? A 25% Part (do What is the flux through the forth surface, S4, in Nm3c? E 93 91 94 Otheexpertta.com Grade Summary Deductions Potential 100% Submissions Attempts remaining 7 3% per attempt detailed view

Explanation / Answer

Given charges are

   q1 = 7 nC

   q2 = -7 nC

   q3 = 16 nC

   q4 = -17 nC

we know that
From Gauss law

the electric flux through the closed surface area is equal to (1/epsilon not ) times the total charge enclosed by the closed surface area

   phi = (1/epsilon not)(Q_in)

part a

  
   The charge q_in enclosed by the surface S1 is q1_in = q1 = 7 nC

so the electric flux is Phi_1 = (1/epsilon not)(q1_in)

               = (1/8.85418782*10^-12)(7*10^-9) Nm2/C

               = 790.58635 Nm2/C

Part b

  
   The charge q_in enclosed by the surface S2 is q2_in = q1+q2 = 7 nC - 7 nC = 0 C

so the electric flux is Phi_2 = (1/epsilon not)(q2_in)

               = (1/8.85418782*10^-12)(0) Nm2/C

               = 0 Nm2/C

Part C

  
   The charge q_in enclosed by the surface S3 is q3_in = q2+q3 = -7 nC + 16 nC = 9 nC

so the electric flux is Phi_3 = (1/epsilon not)(q3_in)

               = (1/8.85418782*10^-12)(9*10^-9) Nm2/C

               = 1016.4682 Nm2/C
Part d

  
The charge q_in enclosed by the surface S4 is q4_in = q1+q2+q3+q4 = 7nc-7 nC + 16 nC-17 nC = -1 nC

so the electric flux is Phi_4 = (1/epsilon not)(q4_in)

               = (1/8.85418782*10^-12)(-1*10^-9) Nm2/C

               = -112.941 Nm2/C

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