Six insulating spheres with radius R 10 cm and equally sprea

Six insulating spheres with radius R= 1,0 cm and equally spread charged Q= 13 nC (for each sphere) is arranged symmetrically around the initial point of the coordinate: seperate charge on x-axis in (±d,0,0) where d= 10,0 m and the same as for y and z-axis.

a) Calculate the electric Flux through cubed- shaped Gauss surface with side length L=50 cm and middle in the initial point of the coordinate.

b) what does the cubic in part a) to be big so that the electric flux through the cube will be half of the elctric flux in part a). Argue your answer.

Solution

a) from guass law,

flux = qin/ e0

for cube with length of 50 cm and charges are at distaance of 10cm so all charged
sphere are inside the cube.

qin = 6 x 13 x 10^-9 C

so flux = (6 x 13 x 10^-9 ) / (8.854 x 10^-12) = 8809.58

b)
flux will be half if new_qin = qin/2

this will happen if cube contains only half of the each sphere.

so side of cube = 10 - 1 = 9 cm