Flux - simple integral computation

[quantum13]

Homework Statement

A surface has the area vector A = 2i + 3j. What is the flux of a uniform electric field through it if the field is E = 4i?

2. Homework Equations
Integral calculus, vectors

The Attempt at a Solution

I don't understand why one could do this. The integral is of E and dA, not E and A. How can I use A to determine dA?

This is a crackpot way I thought of

$$\Phi = \int \vec{E} \cdot \vec{dA}$$

$$\Phi = \vec{E} \cdot \int \vec{dA}$$

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

Then Phi = 4i dot (2i + 3j) = 8 flux units

This seems like wild fantasy though as I don't know if I can pull out a constant from a dot product integral

 

[kuruman]

There is no dA to speak of. You are given A which is the same everywhere and E which is uniform. Just take the dot product as you have in your third equation. There isn't much to this problem/

 

[tomcue]

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Your approach is correct. The integral for flux is given by the dot product of the electric field and the area vector, which in this case is simply the dot product of E and A. This is because the electric field is uniform and perpendicular to the surface, so the magnitude of the electric field is constant over the entire surface. Therefore, we can pull out the constant E and integrate only the area vector to get the flux. Your calculation of 8 flux units is correct.