5654709473

y

Figurę 24.5 A closed surfacc in the shape of a cube in a uniform electric field oricnied parallel to the xaxis. The net flux through the closed surfacc is zero. Side © is the bonom of the cube, and side ® is opposite side (D.

For ©, E is constant and directed inward but dA\ is directed outward (0 = 180°); thus, the flux through this face is

I E-rfA = J £(cos 180°)rfA = -£^ rfA = -EA = -Et²

because the area of each face is .4 = €².

For ©, E is constant and outward and in the same direc-tion as (IA<>{6 = 0°); hence, the flux through this face is

| E • d\ = J E(cos 0°) dA = E ^ dA = +EA = Et²

Therefore, the net flux over all six faces is

0

= _ IX² +    ² + o + 0 4- 0 + 0 =