Electric Force, Equilibrium Config of Charges

[Swagger]

Find the charge Q that should be placed at the centre of the square of side 7.70E+0 cm, at the corners of which four identical charges +q = 11 C are placed so that the whole system is in equilibrium.

(picture attached)

I know that the sum of all the forces must equal zero. I also figured out that the force on the small q's is 1.834E14. Where do I go from here?

 

[Doc Al]

I also figured out that the force on the small q's is 1.834E14.

I assume this is the force (in N?) on each small q due to the other 3 small q's? What direction is this force?

Next step: When you add Q in the middle, the force it exerts on each q better exactly cancel out the other forces. So what force must it exert on q?

 

[Swagger]

I got the force of the small q by using F=k*q*q/r^2

I'm still not sure what to do. Do I multiply the small q Force by 4 and use the same quation to get the charge for big Q?

 

[Swagger]

oh and to answer your question...is it -1.83E14N?

 

[nrqed]

I got the force of the small q by using F=k*q*q/r^2

I'm still not sure what to do. Do I multiply the small q Force by 4 and use the same quation to get the charge for big Q?

I am not sure how you got that but...

You must first find the net force on one small q due to the other 3 charges (for example, pick the one at the left upper corner). You must do a *vector* addition of the 3 forces. Once you have that, you can figure out what must be Q so that the force produced by Q on the upper left small q cancels the force produced by the other three charges q.

But one step at a time.

First, ignore Q. Can you calculate the net force on the upper left charge q produced by the other three charges q? You have to calculate the three forces separately and then do a vector addition of them. Can you do that?

 

[Doc Al]

I got the force of the small q by using F=k*q*q/r^2

That's just the force between two adjacent small q's. You need to find the total force on each q, from each of the other charges.

Pick one of the q's (they'll all have the same force) and find the force from each of the other q's on it. Add those forces to get the total force from the 3 small q's. (Remember that the forces are vectors.) Then add in the big Q to cancel that force.

 

[Swagger]

ok...so here is something I tried.
F(q)=1.834E14 N

Fcos45+Fcos45+Fcos45+F(Q)=0
F(Q)=-(Fcos45+Fcos45+Fcos45)

I get the distance from big Q to little q to be 0.054447m=r.

I then plug in the F(Q) and r into F=k*q*q/r^2

I get -11.66C is this correct?

 

[nrqed]

ok...so here is something I tried.
F=1.834E14 N

This is the force between which pair of charges?
The magnitude between all the different pairs of small q's is NOT the same! Because the distances are not all the same!

Let's say we start with the one in the upper left and label them charges #1, #2, #3 and #4, going clockwise. Then you must calculate the magnitude of the force between q1 and q2, then between q2 and q3 and then between q1 and q4 (actually, this last result will be the same as between q1 and q2 because the charges are the same and the distance is the same).

Fcos45+Fcos45+Fcos45+F(Q)=0

No, that is incorrect. You must look at the direction of the three forces separately and break them into their x and y components. But first, get the magnitudes.