What Is the Value of Point Charge q in a Square Configuration?

[Clara Chung]

Homework Statement

PQRS is a square. Three point charges -Q, +Q and -3Q are fixed at P, Q and S respectively as shown.

A point charge q is then placed at R and it experiences a net electric force towards S. Which of the following is equal to q?

photo :
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Homework Equations

F=kq1q2/r^2

The Attempt at a Solution

in any kind of calculation, Q and q are canceled out and undetermined ,ie : (k1) (q) (Q) / (r1)^2 = (k2) (q) (Q) / (r2)^2, (turn force PR to vertical and horizontal component cancel the vertical component with force QR) . I have no idea on the question or maybe the question itself has mistakes ?The right answer is q=1/9 Q.

 

[cnh1995]

I think any value of q (+ve) will do since the distances are fixed.

 

[Delta2]

Vertical component of force PR cancels force QR. Horizontal component of force PR and force SR add up along SR and hence, the resultantant is directed towards S. All you need to do is use trigonometry to calculate the respective components, with only one unknown q. How is q undetermined?

But suppose vertical component of force PR is $-cos(\pi/4)kQq/r_1^2$ so since it is canceled by force QR we 'll have
$-cos(\pi/4)kQq/r_1^2+kQq/r_2^2=0$. Isnt the product Qq simplified by this last equation?

 

[cnh1995]

But suppose vertical component of force PR is $-cos(\pi/4)kQq/r_1^2$ so since it is canceled by force QR we 'll have
$-cos(\pi/4)kQq/r_1^2+kQq/r_2^2=0$. Isnt the product Qq simplified by this last equation?

Yes. I was about to edit..

 

[Clara Chung]

Thanks a lot for answering this question. I think the question may have mistakes itself. I hope I can get some help with the last stupid question that I've posted too. Thanks.