## anonymous 4 years ago how can i calculate the charge on a point q, given the net electric force and the values of 2 other charges?

1. anonymous

you've got to show the whole question mam

2. NotTim

You should add the given info into a diagram and/or redraw the diagram.

3. anonymous

maybe this will help ;)

4. NotTim

Yup. I can't really much though. I can't remember much from this,=.

5. NotTim

Eashmore, can you do anything here?

6. anonymous

I can do it.

7. anonymous

We have to balance forces. We know the expression for electromagnetic force is$F_E = k_e {q_1 q_2 \over r^2}$ First, let's find the component of the net force that acts in the x and y-directions. $F_{x,3} = F_3 \cos(\theta)$$F_{y,3} = F_3 \sin(\theta)$ We note that both forces act positive in their respective directions. Since $$q_1$$ is positive and located to the left of $$q_3$$, $$q_3$$ must be positive if the force from $$q_1$$ on $$q_3$$ is to be in the positive x-direction. The same thought process verifies this when relating $$q_2$$ and $$q_3$$. Additionally, let's note that the force from $$q_1$$ acts on $$q_3$$ solely in the x-direction, and $$q_2$$ acts on $$q_3$$ solely in the y-direction. Let's balance the forces in x and y-directions now. $F_{x,3} = k_e {q_1 q_3 \over r^2}$and$F_{y,3} = k_e {q_2 q_3 \over r^2}$

8. anonymous

ok this makes sense so far

9. anonymous

You should be able to rearrange the last two equations for $$q_3$$. You should get the same value.

10. anonymous

what do you mean? set them equal? or factor q3 out of the equation?

11. anonymous

Pick one and solve it for $$q_3$$. If we solved both for $$q_3$$, both equations should produce the same value for $$q_3$$.

12. anonymous

Fx^2 + Fy^2 = 30.187 ^2 ? and sub both equations in for Fx and Fy

13. anonymous

I have two unknowns in the above equations yes? so how do I solve for Q3?

14. anonymous

15. anonymous

factoring?

16. JamesJ

You only have one unknown: $$q_3$$. You know q1 and q2; you know r for each equation; and you know the constant $$k_e$$. So you only need to solve for q3.

17. JamesJ

(Notice the r=1 m for one of the forces, and r=2m for another force)

18. JamesJ

In other words, for both of the equations .... the only variable you don't know is q3. So you can use either equation to solve for q3.

19. JamesJ

talk to me ... what's not making sense?

20. JamesJ

ok ...I'm out here of here then.

21. anonymous

i do not know Fx or Fy I only know the sum of both..sorry having internet problems

22. anonymous

You know $$F_x$$ and $$F_y$$. Take the total force as being $$F_3$$, then use the trigonometric relations I gave you for $$F_x$$ and $$F_y$$. $F_x = F_3 \cos(\theta) ~ {\rm and} ~ F_y = F_3 \sin(\theta)$