Finding magnitude of electric field at center of square

[s-f]

In each situation below, electric charges are arranged at the corner of a square. Each charge Q has the same magnitude with the signs indicated in the diagrams. Rank the electric potential from most positive to most negative, and the magnitude of the electric field at the center of the square.

So basically there are 10 squares; each has a charge in each corner. I know how to calculate the electric potential of each square, but not the electric field. I know this involves vectors which is something I don't know anything about (not sure what i hat or j hat mean). For example, here is 1 square:

(+)(+)
( -)( -)

2 positive charges on top, 2 negative ones on bottom. The Voltage/electric potential is clearly 0. How is the magnitude of the electric field calculated?

E = kq/r²

 

[CFede]

You can actually solve this square without using vectors, just some geometry.

You have four electric fields (one for each charge). Two of them point to the lower right corner and the other two point to the lower left corner. All of this fields can be easily computed using the formula you gave.

Now the thing is, once you have the field produced by each charge, how do you get the total field. THe thing to notice here is that the fields form a 90º angle between them, so you have an square triangle. You can just use pythagoras theorem to get the total field.

 

[s-f]

How do you know that 2 point to the lower right corner and that 2 point to the low left?

 

[CFede]

Well, the electric field always points in the direction positive charges would move under its action.

So te two positive charges should move a positive charge away from them, and the two negative ones should move it towards them. Think of it a little, watch the drawing and its pretty clear that two point to the loewr right and the other two to the lower left.

 

[s-f]

Ok I think I get it - you don't need vectors or even geometry really, since they're simply asking to rank by magnitude - I just drew arrows for each charge and compared each box visually to get the answers. Thanks for your explanation.