To determine the electric flux through sphere 'A', we can apply Gauss's Law, which states that the electric flux
φ through a closed surface is equal to the charge
Q‌enc ‌ enclosed by that surface divided by the permittivity of free space
ε0.
For sphere 'A', which passes through the center of the dipole, the enclosed charge is only the negative charge
−q, since the positive charge
+q lies outside of sphere ' A '.
Thus, the electric flux through sphere '
A ' is calculated as:
φ‌sphere ‌‌‌A=‌This result indicates that sphere 'A' encloses a net negative charge, contributing to a negative flux value.