Question

In Fig. 16-61, three objects, O1 and O3 are charged. And O2 is neutral. Suppose the flux through the surface A1 that encloses all three objects is -5.80 105 N·m2/C, and the flux through the surface A2 that encloses the third object only is 1.20 105 N·m2/C. Find the charges O1, O2, O3 carry respectively.

(a) O1: µC
(b) O2: µC
(c) O3: µC

Answer 1

flux through the surface A2 that encloses the third object only is =2.80*10^5 N·m2/C

from guass law flux through a surface = Q enclosed /epsilon

=1.2*10^5 = Q3/epsilon

Q3 = (1.20*10^5)*( 8.85 × 10-12) = 10.26*10^(-7) C = 102.6µC

and given Q2 is neutral so charge = 0 C

and flux through surface A1 = -5.8 *10^5 N·m2/C
which enclosed all the charges

so( Q1+Q2+Q3)/(epsilon) = 1.2 *(10^5 )

Q1+Q2+Q3 = -5.8 *(10^5 )*( 8.85 × 10-12) = -51.33*10^(-7) C

Q3 =10.26*10^(-7) CC and Q2 =0

so Q1 = ( -51.33-10.26)*10^(-7) C = -61.59*10^(-7) C =-615.9 µC