Physics help please!...my lovers?

Question

Gauss's Law

a flat circle of radius 18 cm is placed in a uniform electric field of magnitude 5.8 x 10^2 N/C. What is the electric flux through the circle when its face is (a) perpendicular to the field lines (b) at 45 degrees to the field lines, and (c) parallel to the field lines?

Please provide step-by-step work if possible. Thank you!

Answer 1

Gauss's law states
Flux = surface integral \vec(E) . \vec(dA)
where \vec{E} is the electric field, \vec(dA) is the area on the closed surface S with an outward facing surface normal defining its direction. The point indicates the inner product between the vectors.

In this case Flux = E dA cos(theta) where
theta is the angle between the vectors = a) 0, b) 45, c) 90 degree
cos(theta) = 1, 0.7071, 0
E = 5.8 x 10^2 N/C
dA = pi 18^2 cm^2 = 0.102 m^2

Multiplying the numbers we find 59.2 N m^2/C in the first case, 41.8 N m^2/C in the second case and zero in the third case.