A charge 5.00 nC is placed at the origin of an xy-coordinate system, and a charg

Question

A charge 5.00 nC is placed at the origin of an xy-coordinate system, and a charge -1.97 nC is placed on the positive x-axis at x = 4.04 cm . A third particle, of charge 6.04 nC is now placed at the point x = 4.04 cm ,y = 3.00 cm

Find the x-component of the total force exerted on the third charge by the other two.
Find the y-component of the total force exerted on the third charge by the other two.
Find the magnitude of the total force acting on the third charge and the direction of the total force acting on the
third charge

please try to show as much of your work as possible so I can learn how to solve the other problems like this one, thank you

Explanation / Answer

(a). F31 = kq1 q3/r²
F31 = (9 * 10^9)(5 * 10^(-9))(6.04 * 10^(-9))/(0.0503)² {4.04/5.05,3/5.05}
F31 ={8.63 *10^-5 N , 6.41 * 10^-5 N}

F32 = kq2 q3/r²
F32 = (9 * 10^9)(1.97 * 10^(-9))(6.04 * 10^(-9))/(0.03²) {0,-1}
F32 = {0, -1.19 *10^(-4)} N

R = F31 + F32
R = {8.63 *10^-5 N , 6.41 * 10^-5 N} + {0, -1.19 *10^(-4)} N
R = {8.63 , -5.49} *10^(-5) N

X = 8.63 *10^(-5) N
Y = -5.49 *10^(-5) N

(b). |R|² = (8.63 *10^(-5))² + (-5.49 *10^(-5))²
|R| = 10.23 * 10^(-5) N

(c). tan = -5.49/8.63 = -0.636

= -32.46°

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