One-fourth of a sphere of radius R is removed as shown in figure. An electric field E exists parallel to the xy plane. Find the flux through theremaining curved part.

ϕplain+ϕcurve=0  or  ϕplain=−ϕcurveA→1=−πR22i^,  A→2=−πR22j^E→1=Ecos450i^+E  sin 450j^=E2i^+E2j^ϕ=E→.(A→1+A→2)=−E2πR22−E2πR22=−πR2E2This is the flux entering. So flux is πR2E2