How Does Coulomb's Law Apply to Electric Fields at Points A and B?

[Shakas]

Homework Statement

Use Coulomb's law to determine the magnitude and direction of the electric field at points A and B in Fig. 16-57 due to the two positive charges (Q = 8.0 µC) shown. Is your result consistent with Fig. 16-31b?

Figure 16-57

Figure 16-31b

A)Find the magnitude of the electric field at point A and direction.
B)Find the magnitude of the electric field at point B and direction.

Homework Equations

E=kQ/r^2

The Attempt at a Solution

A)
Let the left Q charge be Q1
Let the right Q charge be Q2

I started by finding the distance vector between Q1 and A, which is the same for Q2 and A.

sqrt((0.1^2)+(0.05^2))=.111m

I then found the electrical field between Q1 and A, which is the same for Q2 and A, but in the opposite direction.

E=(9e9)(8e-6)/(.111^2)=5.84e6

I then split the electrical field into x and y components. Used law of sines to find the angle.

sin(90)/(.111)=sin(x)/(.05)

x=26.8 degrees

Splitting into x and y components:

Q1 to A.
5.84e6*sin(27)=2.651e6 up
5.84e6*cos(27)=5.203e6 right

Q2 to A.
5.84e6*sin(27)= up
5.84e6*cos(27)=5.203e6 left

The x-components cancel due to opposite directions and the y-components are combined.

2.651e6 + 2.651e6 = 5.3e6 N/C 90 degrees above the horizontal.

This is apparently the wrong answer and I do not know what I am doing wrong...

B)
I'm not going to attempt B until I get part A right...

 

[mjsd]

interesting, I don't see a problem with your workings either