# Determining an electric field in vector form, got the answer, just checking.

mr_coffee
Hello everyone, I finally finished the chapter and now I'm going to attempt to do some problems. Well the first problem says: A surface has the are vector A = (2$\hat i + 3\hat j$m^2. What is the flux of a uniform electric field through it if the field is (a) E = 4$\hat iN/C$ (b) $E = 4\hat k$. The answer for (a) is 8 Nm^2/C (b) 0. The answer is 8 for the first one because well (4)(2)...the j component isn't used at all because why? Also b is 0 because k isn't in the same vector as i or j, is that right or am i getting lucky?

$$\Phi_{E} = \vec{E} \cdot \vec{A}$$
So, when you evauluate that and you multiply the j components, you get 3 x 0 which is of course 0. That's the same reason that b. is 0, because $\vec{A}$ has no k component and $\vec{E}$ has no i or j components.