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

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To solve Problem 22, the resultant electrical force on a charge of 1.8*10^-9 C due to two positive point charges of 1.9*10^-9 C each requires calculating the distance using the Pythagorean theorem, yielding r = 0.472 m. The initial calculation of the force was incorrect, likely due to miscalculating the vector components. The correct approach involves using symmetry since the charges are equal and symmetrically placed, simplifying the force calculation. For the direction of the resultant force, vector components should be analyzed rather than relying solely on the tangent function. Understanding these principles will lead to accurate results in calculating electrical forces.
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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?
 
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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.
 
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