An arbitrary surface encloses a dipole. What is the electric flux… - Vidyadip

Question

An arbitrary surface encloses a dipole. What is the electric flux through this surface?

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Answer

Zero.
According to Gauss, law, the electric flux through an enclosed surface is given by $\oint_\text{s}\overrightarrow{\text{E}}.\text{d}\overrightarrow{\text{S}}=\frac{\text{q}_\text{enclosed}}{\in_0}$
The net charge on a dipole is given by $-q + q = 0,$ hence $q_{enclosed }= 0$
Hence the electric flux through a surface enclosing dipole $=\frac{\text{-q}+\text{q}}{\in_0}=\frac{\text{q}}{\in_0}=0.$

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