Find the direction and magnitude of the net electrostatic force exerted on the p

Question

Find the direction and magnitude of the net electrostatic force exerted on the point charge q2 in the figure. (Figure 1) Let q=+2.2?C and d=36cm.

So, I clearly don't understand how to do this problem consistently without plugging it into the calculator incorrectly. I eventually did get the correct answer for part A (though after my tries were up), but still can't get the correct answer for Part B. Any assistance would be helpful. I would put my work here, but think it might be wrong so I don't want to mess people up.

Thanks!

Explanation / Answer

force on q2 due q1 = k*q1*q2/d^2 = 9*10^9*2.2*10^(-6)*2*2.2*10^(-6)/(0.36)^2 = 0.673 N

direction is - y axis

so force on q2 due to q1 (F21) = - 0.673 j

force on q2 due q3 = k*q3*q2/d^2 = 9*10^9*3*2.2*10^(-6)*2*2.2*10^(-6)/(0.36)^2 = 2.02 N

direction is - x axis

so force on q2 due to q3 (F23) = - 2.02 i

magnitud of electric force on q2 due to q4(F24) = k*q4*q2/(sqrt(2)*d)^2 = 9*10^9*4*2.2*10^(-6)*2*2.2*10^(-6)/(2*(0.36)^2) = 1.35 N

x component of F24 = 1.35*sin(-45) = - 0.954 N

y component of F24 = 1.35*cos(-45) = 0.954 N

F24 = - 0.954 i + 0.954 j

net electric field on q2 = - 0.673 j - 2.02 i - 0.954 i + 0.955 j = - 2.974 i + 0.282 j

magnitude = sqrt (2.974^2 + 0.282^2) = 2.99 N

(theta) = arctan(0.282/(-2.974)) = - 5.4 deg

5.4 deg clockwise from -x axis = 174.6 deg counterclock wise from x axis

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