How to Calculate and Measure Electrical Forces: Point Charges Problem 22

[mustang]

Problem 22.
Two positive point charges, each of which has a charge of 1.9*10^-9C, are located at y=0.38m and y=-0.38m.
a. Find the magnitude of the resultant electrial force on a charge of 1.8*10^-9 C located at x=0.28m. Answer in N.
Note: I used a^2+b^2=c^2 to find r in Coluomb's law which I got as 0.472016949. From that I added F_1+F_2 to get 0.0000000276N which was wrong, what did I do wrong?
b. What is the direction of this force(measured from the positive x-axis, with counterclockwise positive)? Answer in degrees.
Note: Would I find the angle by dividing the two electric force answers and times by tan-1?

 

[HallsofIvy]

No, you should, in general, use the fact that a vector, of length v, making angle θ with the x-axis has x-component v cosθ and y-component v sinθ then add the two vector component wise.
Another way is to use the sin law in the triangles formed.

Actually, in this case, the answer is very simple: since the charges are the same and are symmetrically placed, use symmetry.

 

[mustang]

Answer

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