Question

A hemispherical body of radius r is placed in a uniform electric field e. What is the flux linked with the curved surfaces when the field lines are perpendicular to the base.

Answer 1

you know a very important concept , “ net electric flux linked with the closed surface equals zero. ”

so, net electric flux through the hemispherical body = 0

or, electric flux through curve surface + electric flux through plane (base of hemispherical body )  = 0

or, electric flux through curve curve surface = - electric flux through plane.

As shown in figure, electric field is perpendicular on base and area vector is also perpendicular on base but just opposite in direction of electric field.

so, angle between electric field and area vector , $\theta=180^{\circ}$

so, electric flux through plane = E.Acos180° = -EA = -E(πr²)

[ base area, A = πr²]

so, electric flux through curve surface = -(-Eπr²) = Eπr²