Superposition of electrostatic forces?

Question

Four particles with charges of 1.00 μC, −2.00 μC, 3.00 μC, and −4.00 μC are located at the points (0, 0), (2.00, 0) cm, (2.00, 4.00) cm, and (0, 4.00) cm, respectively. What is the magnitude (in N) and direction of the total force they exert on a particle of charge 5.00 μC located at (1.00, 2.00) cm?

Ok, I have been informed that my approach is correct. I calculated and added to zero y-components of all vectors. In the same way I have to add their x components, using for each F = kq1q2/r^2 and Fx = Fcos(theta). To figure out thetas, I need to use the geometry of charges from the force diagram that I need to draw.

Anyways, I have determined that the direction is in the -x direction, but I do not have the magnitude. I am looking for an exact number as I have the equation set up correct already, Can anyone help me, please?

Answer 1

I think the best way to approach this is with straight up vector addition.

First try it with just on charge.

the charge at 0,0 and the test charge at 1,2.

The force as you know is kq1q2/r^2 in the direction (1x+2y) since it is repulsive where x and y denote the unit vectors.

so the force equation which includes direction is 5uC*k/5*(1x+2y). the distance r^2 is from pythagoren thingy 1^2+2^2=5.

So now you have a force equation that gives you direction and magnitude. If you want to make it into and angle equation you can from the vectors.

So if you had to do this for all 4 charges you just do the above equation for each one and then add them up using vector addition. When you are done you will have the magnitude and direction.

so if you include the charge at 2,0 you get F =  10uC/5*k*(1x-2y)

In order to find the total force from those 2 charges just add up the forces from the individual charges. you can factor out the k/5 since it is the same for both of them

k/5*(5uCx+10uCy+10uCx-20uCy) = 5uC*k/5 *(3x-2y)

So you have a magnitude and direction. If you want to solve for the magnitude you take square root of the sum of the squares of the vectors. In order to find the direction of the force I just use the fact that positives repel each other.

So now just do that with all 4 and then add them up.

Good luck