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

Question

anonymous · Answer

you've got to show the whole question mam

nottim · Answer

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

anonymous · Answer

maybe this will help ;)

nottim · Answer

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

nottim · Answer

Eashmore, can you do anything here?

anonymous · Answer

I can do it.

anonymous · Answer

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$$F_{y,3} = k_e {q_2 q_3 \over r^2}$$

anonymous · Answer

ok this makes sense so far

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

attachment

anonymous · Answer

factoring?

jamesj · Answer

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.

jamesj · Answer

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

jamesj · Answer

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.

jamesj · Answer

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

jamesj · Answer

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

anonymous · Answer

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

anonymous · Answer

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 $F_y$. $$F_x = F_3 \cos(\theta) ~ {\rm and} ~ F_y = F_3 \sin(\theta)$$