Electrix flux through a hemisphere

[Physicslearner500039]

Homework Statement

A Gaussian surface in the form of a hemisphere of radius R = 5.68 cm lies in a uniform electric field of magnitude E = 2.50 N/C. The surface encloses no net charge. At the (flat) base of the surface, the field is perpendicular to the surface and directed into the surface. What is the flux through (a) the base and (b) the curved portion of the surface?

Relevant Equations

NA

My attempt is for part a
a. The electric field is into the base of the hemisphere and the area vector is coming out of the base
Θ=180
Area of base of the hemisphere is = π * r^2;
Hence the electric flux ∅ = ∫ E.dA;
∅ = E*π*(0.0568^2)*cos(180) = -2.5*π*0.00322= - 0.0253N.m2/C;

b. For the part b; The area of the curved surface of the hemisphere is 2* π * r^2; Θ=0
Hence the ∅ = 2*0.0253 = 0.506N.m2/C;;
But there is some mistake in the part b. Please advise.

 

[Doc Al]

(1) Note that the field is not normal to the curved portion of the surface. (That's your mistake in part b.)
(2) What must the net flux be through both surfaces?

 

[Physicslearner500039]

Ok so can i conclude that since the hemisphere does not have any charge, the next flux through both the surfaces is 0.
∅Base + ∅Curved = 0; ∅curved = -∅Base ; ∅Curved = 0.0253 N.m2/C

 

[Doc Al]

Right!