Q.A uniform electric field of magnitude $1000\ \text{N/C}$ passes through a flat surface of area $0.5\ \text{m}^2$ whose normal makes an angle of $60^\circ$ with the field direction. Find the electric flux through the surface.

Electric flux Phi_E through a surface is a scalar measure of how many electric field lines cross that surface; for a flat area A in a uniform field E, Phi_E = E A cos(theta) = E.A, where theta is the angle between the field and the area's outward normal, with SI unit N m^2 C^-1. Flux is maximum (Phi_E = EA) when the surface faces the field directly (theta = 0), zero when the surface is turned edge-on so it lies parallel to the field (theta = 90 degrees), and can even be negative if the chosen outward normal points generally against the field. For a curved surface in a non-uniform field, the surface is divided into infinitesimal, effectively-flat elements dA, each contributing E.dA, and the total flux is the sum (integral) of these elemental contributions over the whole surface. For a closed surface -- one that ful …