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.

Explanation

We know flux passing through closed surface
`phi = oint vec(E ) . D vec(S ) = (q_(in))/(in_(0))`
(a)
Charge inside hemisphere `q_(in) = 0`
i.e. ` oint vec(E ) . D vec(S ) = 0`
`phi_(curved) + phi_(plane) = 0`
`phi_(curved) + E S cos 90^(@) = 0`
`phi_(curved) = 0`
(b) `phi_(curved) + phi_(plane) = 0`
`phi_(curved) + E S cos 0 = 0`
`phi_(curved) + E . phi R^(2) = 0`
`phi_(curved) = - E . pi R^(2)`