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Q. A gaussian sphere encloses an electric dipole within it. The total flux across the sphere is :

KCETKCET 2006Electrostatic Potential and Capacitance

Solution:

Total electric flux through enclosed surface
$\phi=\frac{q}{\varepsilon_{0}}+\left(\frac{-q}{\varepsilon_{0}}\right)=0$
Note : As Gaussian surface is not a enclosed surface, hence the question should have been 'an enclosed surface' and not a Gaussian surface.