Question

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

Answer 1

Considering the hemispherical body as a closed body with a curved surface (CS) and a plane surface (PS), the total flux `(phi)` linked with the body will be zero, as no charge is enclosed by the body
I,e., `phi = phi_(CS) + phi_(PS) = 0` .. (i)
It implies that number of electric field lines leaving the surface.
(a) When field is parallel to the base,
`phi_(PS) = E xx pi R^(2) cos 90^(@) = 0`
`:.` From (i), `phi = phi_(CS) = 0`
(b) When field is perpendicular ot the base,
`phi_(PS) = E xx pi R^(2) cos 180^(@) = -E pi R^(2)`
`:.` from (i) `phi_(CS) - E pi R^(2) = 0` or `phi_(CS) = E pi R^(2)`