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Question

An arbitrary surface encloses an electric dipole. What is electric flux to the surface?


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Solution

Gauss Theorem:

  • According to Gauss's Law, the total electric flux out of a closed surface equals the charge contained divided by the permittivity.
  • The electric flux in an area is calculated by multiplying the electric field by the area of the surface projected in a plane and perpendicular to the field.

ϕE=Qε0

  • Where, ϕE is electric flux through a closed surface S enclosing any volume V
  • Q is total charge enclosed within V
  • ε0 is dielectric constant of free space
  • If any arbitrary surface encloses a dipole, the net charge is zero.
  • As the dipole is made up of two equal and opposing charges.
  • The electric flux is also zero as:

ϕE=qε0=0ε0=0

Hence, the electric flux to the surface is zero.


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