Problem 19.65 Consider a spherical Gaussian surface and three charges: q1 = 2.01

Question

Problem 19.65 Consider a spherical Gaussian surface and three charges: q1 = 2.01 C , q2 = -3.29 C , and q3 = 4.62 C . Find the electric flux through the Gaussian surface if it completely encloses (a) only charges q1 and q2, (b) only charges q2 and q3, and (c) all three charges.

Part A = Nm2/C

Part B = Nm2/C

Part C = Nm2/C

Part D Suppose a fourth charge, Q, is added to the situation described in part C. Find the sign and magnitude of Q required to give zero electric flux through the surface. Q = C

Explanation / Answer

part A)

Electric flux through the gaussina surface = Qin/epesilon

= (q1+q2)/epsilon

= (2.01*10^-6 + -3.29*10^-6)/(8.854*10^-12)

= -1.44*10^5 N.m^2/C

B)

Electric flux through the gaussina surface = Qin/epesilon

= (q2+q3)/epsilon

= (-3.29*10^-6 + 4.62*10^-6)/(8.854*10^-12)

= 1.50*10^5 N.m^2/C

C)

Electric flux through the gaussina surface = Qin/epesilon

= (q1+ q2+ q3)/epsilon

= (2.01*10^-6 - 3.29*10^-6 + 4.62*10^-6)/(8.854*10^-12)

= 3.77*10^5 N.m^2/C

D) Electric flux through the gaussina surface = Qin/epesilon

0 = (q1+ q2+ q3 + Q)/epsilon

==> Q = -(q1+q2+q3)

= -(2.01 - 3.29 + 4.62)*10^-6

= -3.34 micro C

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