A hemispherical body is placed in a uniform electric field E. What is the flux linked with the curved surface, if field is (a) parallel to base (figure (a)) (b) perpendicular to base (figure (b)).

Explanation

Considering the hemispherical body as a closed body with a curved surface and a plane base (cross-section), the flux linked with the body will be zero as it does not encloses any charge, i.e.,
`phi=phi_(CS)+phi_(PS)=0.........(i)`
(a) As field is parallel to base, the flux linked with base `phi_(PS)=ExxpiR^(2)cos90^(@)=0`
Substituting this value of `phi_(PS)` in Eq. (i), we get: `phi_(CS)=0`
(b) As field is perpendicular to base, the flux linked with base `phi_(PS)=ExxpiR^(2)cos180^(@)=-piR^(2)E`
So substituting this value of `phi_(PS)` in Eq. (i), we get: `phi_(CS)=piR^(2)E`