A disk of radius a4having a uniformly distributed charge 6 C is placed in the x-y plane with its centre at −a2, 0, 0. A rod of length ‘a’ carrying a uniformly distributed charge 8C is placed on the x-axis from x=a4 to x=5a4. Two point charges -7C and 3C are placed at a4, −a4, 0 and −3a4, 3a4, 0 respectively.Consider a cubical surface formed by six surfaces x=±a2, y=±a2, z=±a2. The electric flux through this cubical surface is

From Gauss' Law, we have flux equal toϕ=ΣQenc ε0=8C4−7C+6C2ε0=−2Cε0 ORThe disc is placed with its center at (-a/2, 0, 0). Hence we can say that half of the discs are enclosed within the cube. Therefore, the charge on the disc enclosed within the cube is 6C/2= 3C.The length of the rod is ’a’ with total charge 8C. The surface of the cube lies at a distance of a/2. Therefore the section of the rod enclosed within the cube is a/2-a/4=a/4.Therefore the total charge of the rod enclosed within the cubical surface is 2C. It is to be noted that the charge 3C lies outside the cubical surface. The charge -7C lies within the cubical surface i.e. at (a/4, -a/4, 0).From the above information, the total charge (Q)enclosed within the surface is,Q=3C+2C+−7CQ=−2Cϕ=−2Cε0