Why Do Signs Matter in Calculating Forces Between Charges?

[Bensky]

Another question on electric fields. :(

I have another problem I don't understand on electric fields. I thought I understood these after my last post, but I guess not. I'm guessing it has something to do with the signs of the forces, but I am not sure.

Homework Statement

Particles of charge Q1 = +68 µC, Q2 = +49 µC, and Q3 = -80 µC are placed in a line (Fig. 16-37). The center one is 0.35 m from each of the others. Calculate the net force on each charge due to the other two.

Figure 16-37

Homework Equations

F = KQ_1Q_2/r^2

The Attempt at a Solution

F = K * Q1Q2/r^2
F_12 = (K)(6.8 X 10-5)(4.9 X 10-5)/.35^2
F_12 = 244.8 N (goes to the left, repels)

F_13 = K(Q1Q2)/r^2
F_13 = (K)(6.8 X 10-5)(4.9 X 10-5)/.7^2
F_13 ~= 100 N (goes to the right, attracts)

F_q1 = -244.8 + 100
F_q1 = -144.8 N (wrong)

However, the second part of the question asked which direction it went in, and based on my answer, I put "left" and that was correct. I'm confused.

 

[Snazzy]

What does F_13 mean? 1 on 3 or 1 due to 3?

 

[nrqed]

I have another problem I don't understand on electric fields. I thought I understood these after my last post, but I guess not. I'm guessing it has something to do with the signs of the forces, but I am not sure.

Homework Statement

Particles of charge Q1 = +68 µC, Q2 = +49 µC, and Q3 = -80 µC are placed in a line (Fig. 16-37). The center one is 0.35 m from each of the others. Calculate the net force on each charge due to the other two.

Figure 16-37

Homework Equations

F = KQ_1Q_2/r^2

The Attempt at a Solution

F = K * Q1Q2/r^2
F_12 = (K)(6.8 X 10-5)(4.9 X 10-5)/.35^2
F_12 = 244.8 N (goes to the left, repels)

F_13 = K(Q1Q2)/r^2
F_13 = (K)(6.8 X 10-5)(4.9 X 10-5)/.7^2
F_13 ~= 100 N (goes to the right, attracts)

F_q1 = -244.8 + 100
F_q1 = -144.8 N (wrong)

However, the second part of the question asked which direction it went in, and based on my answer, I put "left" and that was correct. I'm confused.

Watch out! In F_13 you used the charge of q2 instead of q3!

 

[Doc Al]

Your answers look good to me. Since they ask for the direction separately, I suspect that for the first part they just wanted the magnitude of the force.

 

[Doc Al]

Watch out! In F_13 you used the charge of q2 instead of q3!

That was a typo; the answer matches the correct numbers.

 

[nrqed]

That was a typo; the answer matches the correct numbers.

Ah, ok! I should have checked!

To the OP: yes, they surely want the magnitude only. And be careful with sig figs.

 

[Bensky]

Wow. That was dumb of me for not seeing magnitude right next to the problem...thank you everyone in this thread. At least I know what I'm doing now...