Three charges are fixed to an x,y coordinate system. A charge of 18uC is on the

Question

Three charges are fixed to an x,y coordinate system. A charge of 18uC is on the y axis at y =3m. A charge of -12uC is at the origin. Lastly a charge of 49uC is on the x axis at x=3m. Determine the magnitude and direction of the net electrostatic force on the charge at x=3m. Specify the direction relative to the -x axis.

My professor gave us the answer to this question which is F= .416N and the direction is 48.5 below the -x axis. Unfortunately there is not any work shown that goes along with the answer. I was following the work shown on a different website but was unable to get the right direction when I solved the problem. Any help would be greatly appreciated. My work is as follows:

q1=16 uC at y=3m

q2= -12uC at origin

q3= 49 uC at x=3m

F23: 9x10^9 (-12x10^-6)(49x10^-6)/3^2 = .588N with angle of 180 degrees (not sure how this angle was determined)

F13: 9x10^9 (16x10^-6)(49x10^-6)/ (3 sqrt2) ^ 2 = .392N with angle of 315 degrees (not sure how this angle was determined)

Horizontal forces: F23: .588cos180= -.588N, F13: .392cos315 = .277N, so net horizontal force: -.311N

Vertical forces: F23: .588sin180 = 0, F13: .392sin315= -.277N, so net vertical force: -.277N

F= sqrt (.311^2 + .277^2)= .416N

direction: Tan-1 (vertical force/horizontal force) --> tan-1 (.277/.311) = 41.7 degrees below the -x axis

Thank you in advance!

Explanation / Answer

The force on q3 by q1 = k*q1*q2/r^2 (Coulomb's Law)

F31 = (9 x 10^9 x 18 x 10^-6 x 49 x 10^-6) / (3^2 + 3^2)

F13 = 1.87 N

It is directed down and to the right we calculate the angle to be -45 degree [arctan(-3/3) = -45 degree]

So the components of F31 are F31x = F31*cos(-45) = 1.87*cos(-45) = 1.322 N

and F31y = F31*sin(-45) = -1.322N

Now

F32 = k*q2*q3/r^2

F32 = (9 x 10^9 x 16 x 10^-6 x 49 x 10^-6) / 3^2 = 0.784N and is directed to the left

F3x = 1.322 - 0.784 = 0.538 N

F3y = -1.322N

So F3 = sqrt(F3x^2 + F3y^2) = sqrt(0.538^2 + 1.322^2) = 1.427 N

= arctan(F3y/F3x) = arctan(1.322/0.538) = 68 degree

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