I got the answer 37.13047 uC, but I wasn\'t sure if that was correct. Five charg

Question

I got the answer 37.13047 uC, but I wasn't sure if that was correct.

Five charges arc placed in a cloned box. Each charge (except the first) bus a magnitude which is twice that of the previous one placed in the hex. All charges have the same sign and (alter all the charges have been placed in the box) the net electric flux through the box Ls 1.3 times 10^7 N middot m^2/C. What is the magnitude of the smallest charge in the box? The permittivity of a vacuum is 8.85419 times 10^-12 C^2/N middot m^2. Answer in units of mu^C.

Explanation / Answer

electric flux is given by:

phi = Q(enclosed)/epsilon0

1.3 x 10^7 = Q (1 + 2 + 4 + 8 + 16)/8.85 x 10^-12

Q = 1.3 x 10^7 x 8.85 x 10^-12 / 31 = 3.7 x10^-6 C

Hence, Q = 3.7 x10^-6 C = 3.7 uC

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