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?

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Nylex

There's no j component for a. because the j component of the field you're given is 0. You're taking a dot product to find the flux, ie

$$\Phi_{E} = \vec{E} \cdot \vec{A}$$

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.

mr_coffee

ohh!! i forgot all about that, i have to refresh on vector math! thanks!

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