Calculate the Electric Field at One Corner of a Square

[jumbogala]

Homework Statement

One side of a square has length 2.0 cm.

In three of the square's corners, there are point charges.
Top left corner: -1.0 nC (call this A)
Bottom left corner: 10 nC (call this B)
Bottom right corner: -1.0 nC (call this C)

The top right corner has no charge, and is labelled P.

What is the magnitude of the electric field at point P?

Homework Equations

Electric Field = KQ/r²

The Attempt at a Solution

Electric Field Due to A:
K(-1.0 x 10^-9 C)/(0.02 m²) = -22475 N/C, left

Electric Field Due to C:
Same as above, but this time the direction is down

Electric Field Due to B:
First calculate the distance from B to P. This is 0.02²+0.02² = 0.0008. Take the square root of 0.0008 to find 0.0282 m.
K(10 x 10^-9 C) / (0.0282)² = 112375 N/C, at a 45 degree angle pointing north east.

Now, take the sum of all three parts to find the net electric field.
A and C together point south west, with a magnitude of 31784.44 N/C.

112375 N/C - 31784.44 N/C = 80590.55 N/C, north east.

However, the answer given on the page is not what I got. What went wrong?

 

[LowlyPion]

Remember they add like vectors.

 

[jumbogala]

I thought I did add them like vectors.

Adding vectors A (points left) and C (points down) gives a new vector which points south west...

22475^2 + 22475^2 = 1010251250.. take the square root of this and get 31784.44.

Since this vector points the opposite direction as vector B, which is 112375, can't I go 112375 - 31784.44?

 

[LowlyPion]

So you have. Sorry I just calculated it and I get (5 -√2)*22,500 = 80,680

using k = 9*10⁹

So I can't say what they are looking for then.

 

[jumbogala]

I get something similar, but I used K = 8.99x10^9. They are definitely looking for the electric field, but the answer given is 1.1 x 10 ^5.

I think whoever wrote the answer sheet probably made a mistake.

Thanks!

 

[LowlyPion]

I get something similar, but I used K = 8.99x10^9. They are definitely looking for the electric field, but the answer given is 1.1 x 10 ^5.

I think whoever wrote the answer sheet probably made a mistake.

Thanks!

Yes their mistake. They canceled out the -1 nC charges. They don't as described.